def test_skip_arguments(self):
from partial import SKIP
template = "{0} {1} {2} and {3}"
skip_first = partial(template.format, SKIP, 2)
skip_last = partial(template.format, 1, 2, SKIP)
with_two_skips = partial(template.format, SKIP, 2, SKIP)
# Unevaluated skips
with self.assertRaises(Exception):
skip_last()
with self.assertRaises(Exception):
skip_last(3)
with self.assertRaises(Exception):
with_two_skips(1)
with self.assertRaises(Exception):
with_two_skips(1, 2)
# Correct skips
self.assertEqual(skip_last(3, 4), "1 2 3 and 4")
self.assertEqual(with_two_skips(4, 6, 7), "4 2 6 and 7")
self.assertEqual(with_two_skips(4, 7, 8), "4 2 7 and 8")
self.assertEqual(skip_first(1, 3, 4), "1 2 3 and 4")
# Unevaluated skips still don't work
with self.assertRaises(Exception):
skip_last()
with self.assertRaises(Exception):
skip_last(2)
with self.assertRaises(Exception):
with_two_skips(1)
with self.assertRaises(Exception):
with_two_skips(3, 4)
def test_sanity(self):
def foo(x,y,z): return 100*x + 10*y + z
f = partial(foo) # don't bind anything
self.assertEqual(f(1,2,z=3),foo(1,2,z=3))
f = partial(foo,1)
self.assertEqual(f(2,3),foo(1,2,3))
f = partial(foo,1,z=3)
self.assertEqual(f(2),foo(1,2,3))
def test_arguments_held_for_later_execution(self):
def add(x, y):
return x + y
add_3_and_4 = partial(add, 3, 4)
self.assertEqual(add_3_and_4(), 7)
add_3 = partial(add, 3)
self.assertEqual(add_3(7), 10)
add_1_and_4 = partial(add, x=1, y=4)
self.assertEqual(add_1_and_4(), 5)
add_4 = partial(add, y=4)
self.assertEqual(add_4(8), 12)
self.assertEqual(add_4(8), 12) # Calling twice works
def test_nice_string_representation(self):
fake_file = StringIO()
fake_print = partial(print, file=fake_file)
self.assertIn('print', repr(fake_print))
self.assertIn('file', repr(fake_print))
print_one_two_three = fake_print.partial(1, 2, 3)
self.assertIn('print', repr(print_one_two_three))
self.assertIn('file', repr(print_one_two_three))
self.assertIn('1, 2, 3', repr(print_one_two_three))
def test_partial_method(self):
template = "{0} {1} and {2} and {red} {green} and {blue}"
x = partial(template.format, 'purple', 'white')
y = x.partial(green=2, blue=3)
z = y.partial('red', red=1)
w = y.partial('black', blue=4, green=2)
self.assertEqual(
x('pink', green=1, blue=2, red=3),
"purple white and pink and 3 1 and 2",
"Original partial shouldn't change on .partial() method call!",
)
self.assertEqual(z(), "purple white and red and 1 2 and 3")
self.assertEqual(w(red=0), "purple white and black and 0 2 and 4")
self.assertEqual(y(None, red=9), "purple white and None and 9 2 and 3")
def main():
options = sys.argv[1]
# options='010000000'
if int(options) == 0: options = '1' + options[1:]
options = options[0:4] + '0' + options[4:10] # extrema
options = options[0:10] + '0' + options[10] # work,circulation,flux
pick = []
for i in range(len(options)):
if options[i] == '1': pick.append(i)
type1 = pick[random.randrange(0, len(pick))]
# type1=2
# Derivatives
# 0 Partial Derivatives
# 1 Chain Rule
# 2 Directional, and (need to be added) gradient, Tangent Planes
# 3 Lagrange Multipliers
####4 Extrema
# Integrals
# 5-7 Multiple (rectangular, polar, combine spherical/cylindrical) Integrals
# Vectors
# 8 divergence and curl
####9 Line Integrals
####10 Work, Circulation, Flux
# 11 potential functions
# Add later
# 4 Extrema and Saddle Points
# 7'Green’s Theorem'
# 8'Divergence/Stokes Theorem'
master_bank = {}
# partial derivatives
if type1 == 0:
subtype = random.randint(1, 5)
if subtype < 3:
implicit = partial.partial(2, 'mixed')
func = 'f(x,y)'
if subtype >= 3:
implicit = partial.partial(3, 'dummy')
func = 'f(x,y,z)'
f = implicit.f
if subtype == 1 or subtype == 3:
ans = implicit.fx
der = 'f_x'
if subtype == 2 or subtype == 4:
ans = implicit.fy
der = 'f_y'
if subtype == 5:
ans = implicit.fz
der = 'f_z'
probtex = 'Given the function $' + func + '=' + frac(
toTEX(f)) + '$, find $' + der + '$.'
prefix = '$' + der + '=$'
anstex = 'The answer is $' + der + '=' + frac(toTEX(ans)) + '$'
prefix = ''
hint = ''
# Chain Rule
if type1 == 1:
subtype = random.randint(1, 4)
if subtype % 2 == 0:
option = 't'
else:
option = 'uv'
uorv = random.randint(0, len(option) - 1)
der = 'f_%s' % option[uorv]
if subtype < 3:
implicit = partial.partial(2, 'short')
implicit.tuv(option, 2)
f = [implicit.fx, implicit.fy]
func = 'f(x,y)'
df = '(' + f[0] + ')' + '*' + implicit.dtuv[0][
uorv] + '+' + '(' + f[1] + ')' + '*' + implicit.dtuv[1][uorv]
df = df.replace('x', '(' + implicit.tuv[0] + ')')
df = df.replace('y', '(' + implicit.tuv[1] + ')')
if subtype >= 3:
implicit = partial.partial(3, 'short')
f = [implicit.fx, implicit.fy, implicit.fz]
implicit.tuv(option, 3)
func = 'f(x,y,z)'
df = '(' + f[0] + ')' + '*' + implicit.dtuv[0][
uorv] + '+' + '(' + f[1] + ')' + '*' + implicit.dtuv[1][
uorv] + '+' + f[2] + '*' + implicit.dtuv[2][uorv]
df = df.replace('x', implicit.tuv[0])
df = df.replace('y', implicit.tuv[1])
df = df.replace('z', implicit.tuv[2])
if subtype == 1:
probtex = 'Given the function $' + func + '=' + toTEX(
implicit.f) + '$, <br>with $x(u,v)=' + toTEX(
implicit.tuv[0]) + '$ and $y(u,v)=' + toTEX(
implicit.tuv[1]) + '$ find $' + der + '$.'
if subtype == 2:
probtex = 'Given the function $' + func + '=' + toTEX(
implicit.f) + '$, <br>with $x(t)=' + toTEX(
implicit.tuv[0]) + '$ and $y(t)=' + toTEX(
implicit.tuv[1]) + '$ find $' + der + '$.'
if subtype == 3:
probtex = 'Given the function $' + func + '=' + toTEX(
implicit.f) + '$, <br>with $x(u,v)=' + toTEX(
implicit.tuv[0]) + '$, $y(u,v)=' + toTEX(
implicit.tuv[1]) + '$ and $z(u,v)=' + toTEX(
implicit.tuv[2]) + '$ find $' + der + '$.'
if subtype == 4:
probtex = 'Given the function $' + func + '=' + toTEX(
implicit.f) + '$, <br>with $x(t)=' + toTEX(
implicit.tuv[0]) + '$, $y(t)=' + toTEX(
implicit.tuv[1]) + '$ and $z(t)=' + toTEX(
implicit.tuv[2]) + '$ find $' + der + '$.'
import sympy
from sympy.parsing.sympy_parser import parse_expr
t, u, v, x, y, z = sympy.symbols('t u v x y z')
df = df.replace('^', '**')
sympy_exp = parse_expr(df)
ans = str(sympy_exp)
ans = ans.replace('**', '^')
ans = ans.replace('log', 'ln')
# ans=df
prefix = '$' + der + '=$'
anstex = 'The answer is $' + der + '=' + toTEX(ans) + '$'
prefix = ''
hint = ''
# Directional Derivatives
if type1 == 2:
subtype = random.randint(1, 2)
if subtype == 1:
grad = partial.partial(2, 'mixed')
vect = vector.vector(2)
(x, y) = vect.point
evalfx = grad.fx.replace('^', '**')
evalfy = grad.fy.replace('^', '**')
evalfx = evalfx.replace('x', str(vect.point[0]))
evalfy = evalfy.replace('y', str(vect.point[1]))
totalder = (eval(reduce(evalfx)), eval(reduce(evalfy)))
func = 'f(x,y)'
probtex = 'Given the function $' + func + '=' + toTEX(
grad.f
) + '$, find the derivative at $(%d,%d)$ in the direction $ \left\langle %d,%d \\right\\rangle $.' % tuple(
vect.point + vect.vec1)
if subtype == 2:
grad = partial.partial(3, 'dummy')
vect = vector.vector(3)
(x, y, z) = vect.point
grad.fx = grad.fx.replace('x', str(vect.point[0]))
grad.fy = grad.fy.replace('y', str(vect.point[1]))
grad.fz = grad.fz.replace('z', str(vect.point[2]))
totalder = (eval(reduce(grad.fx)), eval(reduce(grad.fy)),
eval(reduce(grad.fz)))
func = 'f(x,y,z)'
probtex = 'Given the function $' + func + '=' + toTEX(
grad.f
) + '$, find the derivative at $(%d,%d,%d)$ in the direction $\left\langle %d,%d,%d \\right\\rangle$.' % tuple(
vect.point + vect.vec1)
roundlim = 4
ans = str(float(vector.dot(totalder, vect.vec1)) / float(vect.norm1))
ans = str(round(
vector.dot(totalder, vect.vec1) / vect.norm1, roundlim))
prefix = ''
anstex = 'The answer is %s $ %s $.' % (prefix, toTEX(ans))
hint = ''
# Lagrange Multipliers
if type1 == 3:
bank = {}
# bank['problem']=['ans','prefix','hint','anstex']
bank[
'Find the maximum volume of a box with a surface area of $24$.'] = [
'8', '$V=$',
'Optimize $f=xyz$ constrained by $g=2xy+2yz+2xz-24=0$.'
]
bank[
'Find the maximum volume contained by a box with a surface area of $12$ with the top missing (5 sides).'] = [
'4', '$V=$',
'Optimize $f=xyz$ constrained by $g=2xy+2yz+xz-12=0$.'
]
# more geo? cylinder?
bank[
'Find the maximum volume of a cylinder inscribed in a sphere with radius $r_s=5$.'] = [
'32*pi', '$V=$', 'Use the constraint $r_s=\sqrt{r^2+(h/2)^2}$.'
]
bank[
'Find the maximum volume of a rectangular prism inscribed in a sphere with a diameter $d_s=3$.'] = [
'1', '$V=$', 'Use the constraint $d_s=\sqrt{x^2+y^2+z^2}$.'
]
bank[
'Maximize the equation $f=xy$, subject to the constraints $x,y>0$ and $x^2+4y^2=50$.'] = [
'25/2', '', ''
]
bank[
'Maximize the equation $f=xy$, subject to the constraint $x+4y=16$.'] = [
'16', '', ''
]
bank[
'Maximize the equation $f=xy^3z$, subject to the constraints $x,y,z>0$ and $x+y+z=5$.'] = [
'27', '', ''
]
bank[
'Maximize the equation $f=xy\sqrt{z}$, subject to the constraints $x,y,z>0$ and $x+y+z=20$.'] = [
'128', '', ''
]
bank[
'Maximize the equation $f=x^2+y^2+z^2$, subject to the constraints $x,y,z>0$ and $x+y+z=6$.'] = [
'12', '', ''
]
bank[
'Maximize the equation $2x-3y$ subject to the constraint $x^2+y^2=13$.'] = [
'13', '', ''
]
bank[
'Maximize the equation $3x-y$ subject to the constraint $x^2+y^2=40$.'] = [
'20', '', ''
]
bank[
'Minimize the equation $x-2y$ subject to the constraint $x^2+y^2=45$.'] = [
'15', '', ''
]
bank[
'Find the minimum distance from the surface $xyz=1$ to the origin'] = [
'3^(1/2)', '', 'Let $f=x^2+y^2+z^2$'
]
bank[
'Find the minimum distance from the surface $x^2y=1$ to the origin'] = [
'(2^(1/3)+2^(-2/3))^(1/2)', '', ''
]
bank[
'Find the minimum distance from the surface $x^3y=1$ to the origin'] = [
'(3^(1/4)+3^(-3/4))^(1/2)', '', ''
]
# to finish (2 each)
bank[
'Find the maximum value of $x+y+z$ if the points lie on the sphere $x^2+y^2+z^2=5$.'] = [
'ans', 'prefix', 'hint', 'anstex'
]
# bank['Find the point on the plane $$ closest to the point $$.']=['ans','prefix','hint','anstex']
probtex = random.choice(bank.keys())
ans_set = bank[probtex]
ans = ans_set[0]
prefix = ans_set[1]
hint = ans_set[2]
if len(ans_set) == 3:
if prefix != '': prefix += ' '
anstex = 'The answer is %s$%s$.' % (prefix, toTEX(ans))
else:
anstex = ans_set[3]
# Extrema
if type == 4:
pass
# Multiple Integrals
if type1 == 5 or type1 == 6 or type1 == 7:
if type1 == 5:
rando = random.randint(1, 4)
if rando == 1:
type2 = 'triple'
else:
type2 = 'double'
elif type1 == 6: # polar
type2 = 'polar'
elif type1 == 7: # cylindrical integrals
type2 = 'sphercyn'
intprob = integral(type2)
probtex = intprob.problem
ans = intprob.ans
anstex = 'The answer is $%s$.' % toTEX(ans)
prefix = ''
hint = ''
# Divergence and Curl
if type1 == 8:
dc = partial.divcurl()
subtype = random.randint(1, 2)
if subtype == 1:
dc.prob = 'divergence'
ans = dc.div
anstex = 'The divergence is $' + toTEX(ans) + '$.'
if subtype == 2:
dc.prob = 'curl'
ans = '<%s,%s,%s>' % (dc.curl[0], dc.curl[1], dc.curl[2])
anstex = 'The curl is $ \left\langle %s, \ %s, \ %s \\right\\rangle $.' % (
toTEX(dc.curl[0]), toTEX(dc.curl[1]), toTEX(dc.curl[2]))
dcftex = []
for i in range(3):
dcftex.append(toTEX(dc.f[i]))
probtex = 'Find the ' + dc.prob + ' of the field described by $ \left\langle %s,%s,%s \\right\\rangle $.' % tuple(
dcftex)
prefix = ''
hint = ''
# Line Integrals
if type1 == 9:
bank = {}
# answer, prefix, hint
# circle x,y
bank[
'Evaluate the integral $\int_C{xy^2 \ ds}$ where $C$ is the path from $(2,0)$ to $(0,2)$ clockwise on $x^2+y^2=4$.'] = [
'16/3', '', ''
]
bank[
'Evaluate the integral $\int_C{xy \ ds}$ where $C$ is the clockwise path from $\\theta=0$ to $\\theta=\pi/2$ on the unit circle.'] = [
'1/2', '', ''
]
bank[
'Evaluate the integral $\int_C{\\frac{1}{x^2} \ ds}$ where $C$ is the clockwise path from $\\theta=0$ to $\\theta=\pi/4$ on the unit circle.'] = [
'1', '', ''
]
bank['Evaluate the integral $\int_C{\\frac{y}{x}\cdot \\frac{1}{x^2} \ ds}$ where $C$ is the clockwise path from $\\theta=0$ to $\\theta=\pi/3$ on the unit circle.'] = [
'1', '',
'After substituting $x(t)=\cos(t)$ and $y(t)=\sin(t)$, you can put the integrand in the form $\sec^2(t)\\tan(t)$, or $\sin(t) / \cos^3(t)$, either of which can be integrated with $u$-substitution.'
]
# line segment
bank[
'Evaluate the integral $\int_C{x-y^2z \ ds}$ where $C$ is the line segment from $(0,0,0)$ to $(2,1,2)$.'] = [
'3/2', '', ''
]
bank[
'Evaluate the integral $\int_C{\pi\cdot\sin(\pi x)-xy \ ds}$ where $C$ is the line segment from $(0,0)$ to $(3,4)$.'] = [
'-50/3', '', ''
]
bank[
'Evaluate the integral $\int_C{xy+z \ ds}$ where $C$ is the line segment from $(-2,-1,0)$ to $(1,3,12)$.'] = [
'169/2', '', ''
]
bank[
'Evaluate the integral $\int_C{\\frac{x}{y}+z \ ds}$ where $C$ is the line segment from $(1,2,1)$ to $(3,6,5)$.'] = [
'21', '', ''
]
bank[
'Evaluate the integral $\int_C{\\frac{z}{xy} \ ds}$ where $C$ is the line segment from $(1,2,3)$ to $(2,3,5)$.'] = [
'sqrt(6)*ln(3)', '', ''
]
bank[
'Evaluate the integral $\int_C{x\cdot\sin(y) \ ds}$ where $C$ is the line segment from $(0,0)$ to $(1,\pi)$.'] = [
'1/pi*sqrt(pi^2 + 1)', '', ''
]
# more complex
bank[
'Evaluate the integral $\int_C{ds}$ where $C$ is the path from $(0,0)$ to $(1,1)$ on $y=x^4$.'] = [
'(17^(3/2)-1)/144', '', ''
]
"""
master_bank['Find the arc length of the curve $y=.75*x$ from $x=0$ to $x=5$.']=['','6.25','']
master_bank['Find the arc length of the curve $y=(x+5)^{3/2}$ from $x=0$ to $x=8$.']=['','988/27','']
master_bank['Find the arc length of the curve $y=\sinh(x)$ from $x=0$ to $x=1$.']=['','(e^2-1)/(2*e)','']
master_bank['Find the arc length of the parametric curve $x=\cos(t)$ $y=\sin(t)$ from $t=0$ to $t=\pi$']=['','pi','']
master_bank['Find the arc length of the parametric curve $x=t^{3/2}$ $y=t$ from $t=0$ to $t=1$']=['','61/27','']
master_bank['Find the arc length of the parametric curve $x=3*t^2$ $y=1/2*t^3$ from $t=0$ to $t=3$']=['','30.5','']
master_bank['Find the arc length of the parametric curve $x=t^3$ $y=t^{4.5}$ from $t=0$ to $t=1$']=['','1.43971','']
"""
# helix
bank[
'Evaluate the integral $\int_C{ xy^2+z \ ds}$ where $C$ is the path along the helix $\\vec{r}(t)=\langle\cos(t), \sin(t), t \\rangle$ for $t=[0,2\pi]$.'] = [
'2*sqrt(2)*pi^2', '',
'You may need to use the identity $\sin^2(x)+\cos^2(x)=1$.'
]
bank[
'Evaluate the integral $\int_C{\displaystyle\\frac{x^2z}{1-y^2} \ ds}$ where $C$ is the path along the helix $\\vec{r}(t)=\langle\cos(t), \sin(t), t \\rangle$ for $t=[0,2\pi]$.'] = [
'2*sqrt(2)*pi^2', '',
'You may need to use the identity $\sin^2(x)+\cos^2(x)=1$.'
]
bank['Evaluate the integral $\int_C{xy+z \ ds}$ where $C$ is the path along the helix $\\vec{r}(t)=\langle\cos(t), \sin(t), t/2 \\rangle$ for $t=[0,4\pi]$.'] = [
'2*sqrt(5)*pi^2', '',
'You may need to use the identity $\sin^2(x)+\cos^2(x)=1$ and you will need integration by parts.'
]
bank['Evaluate the integral $\int_C{x^2 \ ds}$ where $C$ is the path along the helix $\\vec{r}(t)=\langle\cos(t), \sin(t), 2t \\rangle$ for $t=[0,2\pi]$.'] = [
'pi*sqrt(5)', '',
'You may need to use the identity $\sin^2(x)+\cos^2(x)=1$ and $\cos^2(t)=1/2(\cos(2t)+1)$.'
]
# split integrals intdx+intdy+intdz
probtex = random.choice(bank.keys())
ans_set = bank[probtex]
ans = ans_set[0]
prefix = ans_set[1]
hint = ans_set[2]
anstex = 'The answer is %s $%s$.' % (prefix, toTEX(ans))
probtex = probtex.replace('\int', '\displaystyle\int')
# Work, Circulation, Flux
if type1 == 10:
pass
# Potential Functions
if type1 == 11:
subtype = random.randint(1, 2)
if subtype == 1: # (2 variables)
grad = partial.partial(2, 'mixed')
func = 'f(x,y)'
probtex = 'Given the conservative vector field $\\vec{F}=\left(%s\\right)\hat{i}+\left(%s\\right)\hat{j}$, find the potential function $f(x,y)$.' % (
toTEX(grad.fx), toTEX(grad.fy))
if subtype == 2: # (3 variables)
grad = partial.partial(3, 'dummy')
func = 'f(x,y,z)'
probtex = 'Given the conservative vector field $\\vec{F}=\left(%s\\right)\hat{i}+\left(%s\\right)\hat{j}+\left(%s\\right)\hat{k}$, find the potential function $f(x,y,z)$.' % (
toTEX(grad.fx), toTEX(grad.fy), toTEX(grad.fz))
prefix = '$' + func + '=$'
suffix = ' $+c$ '
ans = grad.f
anstex = 'The answer is %s $%s$.' % (prefix, toTEX(grad.f))
hint = ''
if type1 != 11: suffix = ''
print probtex
print ans
print anstex
print prefix
print suffix
print hint
def main():
options = sys.argv[1]
# php issues
# options='00101111'
options = options[4:8] + options[0:4]
if int(options[0:4]) == 0: options = '1' + options[1:]
if int(options[4:8]) == 0: options = options[:4] + '1' + options[5:]
# type 1 is functions, type 2 is derivative type
pick1 = []
for i in range(4):
if options[i] == '1': pick1.append(i)
# makes poly/trig/trans 2x as likely as hypinv
for i in range(3):
if options[i] == '1': pick1.append(i)
pick2 = []
for i in range(4):
if options[i + 4] == '1': pick2.append(i)
type1 = pick1[random.randrange(0, len(pick1))]
type2 = pick2[random.randrange(0, len(pick2))]
# type1=1
# type2=0
# options[0]=poly
# options[1]=trig
# options[2]=trans
# options[3]=hypinv
# options[4]=basic
# options[5]=chain
# options[6]=product
# options[7]=implicit
master_bank = {}
# print options
poly = {}
if type1 == 0 and type2 == 0:
poly['x'] = [
'1',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
poly['x^2'] = [
'2*x',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
poly['x^3'] = [
'3*x^2',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
poly['x^4'] = [
'4*x^3',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
poly['x^5'] = [
'5*x^4',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
poly['x^6'] = [
'6*x^5',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
poly['x^pi'] = [
'pi*x^(pi-1)',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
poly['x^e'] = [
'e*x^(e-1)',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
# fraction
poly['x^(1/2)'] = [
'1/2*x^(-1/2)',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
poly['x^(1/3)'] = [
'1/3*x^(-2/3)',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
poly['x^(7/3)'] = [
'7/3*x^(4/3)',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
poly['x^(-1/2)'] = [
'-1/2*x^(-3/2)',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
poly['x^(-1/3)'] = [
'-1/3*x^(-4/3)',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
# 1/over
poly['1/x'] = [
'-1/x^2',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
poly['1/x^2'] = [
'-2/x^3',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
poly['1/x^1.3'] = [
'-1.3*x^(-2.3)',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
poly['x^100'] = [
'100*x^99',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
# decimal
poly['x^1.2'] = [
'1.2*x^(.2)',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
poly['x^.1'] = [
'.1*x^(-.9)',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
# combination
poly['x^3+x^(1/3)'] = [
'3*x^2+1/3*x^(-2/3)',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
poly['x+1/x'] = [
'1-1/x^2',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
poly['x^2+2*x+1'] = [
'2*x+2',
'Use the <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=1" target="_blank">Power rule</a> for derivatives.'
]
master_bank.update(poly)
trig = {}
if type1 == 1 and type2 == 0: # options[1]=='1' and options[4]=='1':
trig['sin(x)'] = [
'cos(x)',
'Use <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=3" target="_blank">this</a> table for trigonometric derivatives.'
]
trig['cos(x)'] = [
'-sin(x)',
'Use <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=3" target="_blank">this</a> table for trigonometric derivatives.'
]
trig['tan(x)'] = [
'sec(x)^2',
'Use <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=3" target="_blank">this</a> table for trigonometric derivatives.'
]
trig['sec(x)'] = [
'sec(x)*tan(x)',
'Use <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=3" target="_blank">this</a> table for trigonometric derivatives.'
]
trig['csc(x)'] = [
'-csc(x)*cot(x)',
'Use <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=3" target="_blank">this</a> table for trigonometric derivatives.'
]
trig['cot(x)'] = [
'-csc(x)^2',
'Use <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=3" target="_blank">this</a> table for trigonometric derivatives.'
]
master_bank.update(trig)
trans = {}
if type1 == 2 and type2 == 0:
trans = master_bank
trans['e^x'] = [
'e^x',
'Use <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=4" target="_blank">this</a> rule for exponential derivatives.'
]
trans['ln(x)'] = [
'1/x',
'Use <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/basicrules&page_id=4" target="_blank">this</a> rule for logarthmic derivatives.'
]
master_bank.update(trans)
hypinv = {}
if type1 == 3 and type2 == 0:
hypinv['asin(x)'] = ['1/(1-x^2)^(1/2)', '']
hypinv['acos(x)'] = ['-1/(1-x^2)^(1/2)', '']
hypinv['atan(x)'] = ['1/(1+x^2)', '']
hypinv['asec(x)'] = ['1/(x*(1-x^2)^(1/2))', '']
hypinv['acsc(x)'] = ['-1/(x*(1-x^2)^(1/2))', '']
hypinv['acot(x)'] = ['-1/(1+x^2)', '']
hypinv['sinh(x)'] = ['cosh(x)', '']
hypinv['cosh(x)'] = ['sinh(x)', '']
hypinv['tanh(x)'] = ['sech(x)^2', '']
hypinv['sech(x)'] = ['-sech(x)*tanh(x)', '']
hypinv['csch(x)'] = ['-csch(x)*coth(x)', '']
hypinv['coth(x)'] = ['-csch(x)^2', '']
master_bank.update(hypinv)
# poly(poly)
chain = {}
if type1 == 0 and type2 == 1:
chain['(3*x-1)^3'] = ['9*(3*x - 1)^2', '']
chain['(5*x-3)^10'] = ['50*(5*x - 3)^9', '']
chain['(2*x^2-7*x+1)^3'] = ['3*(4*x-7)*(2*x^2-7*x+1)^2', '']
chain['1/(3*x^2+1)'] = ['-(6*x)/(3*x^2 + 1)^2', '']
chain['2/(x^5-x^2)^3'] = ['(6*(2*x - 5*x^4))/(x^2 - x^5)^4', '']
chain['(x^2-1)^3.1'] = ['6.2*x*(x^2-1)^(2.1)', '']
# trig(trig)
if type1 == 1 and type2 == 1:
chain['sin(sin(x))'] = ['cos(x)*cos(sin(x))', '']
chain['sin(cos(x))'] = ['-sin(x)*cos(cos(x))', '']
chain['sin(tan(x))'] = ['sec(x)^2*cos(tan(x))', '']
chain['sin(sec(x))'] = ['sec(x)*tan(x)*cos(sec(x))', '']
chain['sin(csc(x))'] = ['-csc(x)*cot(x)*cos(csc(x))', '']
chain['sin(cot(x))'] = ['-csc(x)^2*cos(cot(x))', '']
chain['cos(cos(x))'] = ['sin(x)*sin(cos(x))', '']
chain['cos(sin(x))'] = ['-cos(x)*sin(sin(x))', '']
chain['cos(tan(x))'] = ['-sec(x)^2*sin(tan(x))', '']
chain['cos(sec(x))'] = ['-sec(x)*tan(x)*sin(sec(x))', '']
chain['cos(csc(x))'] = ['csc(x)*cot(x)*sin(csc(x))', '']
chain['cos(cot(x))'] = ['csc(x)^2*sin(cot(x))', '']
chain['tan(tan(x))'] = ['sec(x)^2*sec(tan(x))^2', '']
chain['tan(sec(x))'] = ['sec(x)*tan(x)*sec(sec(x))*tan(sec(x))', '']
chain['tan(csc(x))'] = ['csc(x)*cot(x)*csc(csc(x))*cot(csc(x))', '']
chain['tan(cot(x))'] = ['csc(x)^2*csc(cot(x))^2', '']
# ln(ln)
if type1 == 2 and type2 == 1:
chain['ln(ln(x))'] = ['1/(x*ln(x))', '']
chain['e^(e^x)'] = ['e^x*e^(e^x)', '']
chain['2^(2^x)'] = ['ln(2)^2*2^x*2^(2^x)', '']
# ln(poly)
if options[0] == '1' and options[2] == '1' and type2 == 1:
chain['ln(2*x)'] = ['1/x', '']
chain['ln(x^2)'] = ['2/x', '']
chain['ln(x^3)'] = ['3/x', '']
chain['ln(3*x^2+2*x)'] = ['(6*x+2)/(3*x^2 + 2*x)', '']
chain['ln((x-1)^2)'] = ['2/(x-1)', '']
chain['ln(1/x)'] = ['-1/x', '']
# poly(ln)
chain['ln(x)^2'] = ['2*ln(x)/x', '']
chain['ln(x)^3'] = ['3*ln(x)^2/x', '']
chain['1/ln(x)'] = ['-1/(x*ln(x)^2)', '']
chain['1/ln(x)^2'] = ['-2/(x*ln(x)^3)', '']
chain['ln(x)^1.3'] = ['ln(x)^.3/x', '']
if options[1] == '1' and options[2] == '1' and type2 == 1:
# ln(trig)
chain['ln(sin(x))'] = ['cot(x)', '']
chain['ln(cos(x))'] = ['-tan(x)', '']
chain['e^(sin(x))'] = ['cos(x)*e^(sin(x))', '']
chain['e^(sin(x)^2)'] = ['2*sin(x)cos(x)*e^(sin(x)^2)', '']
chain['e^(cos(x))'] = ['-cos(x)*e^(cos(x))', '']
chain['2^(sin(x))'] = ['ln(2)*cos(x)*2^(sin(x))', '']
# trig(ln)
chain['sin(ln(x))'] = ['cos(ln(x))/x', '']
chain['sin(e^x)'] = ['e^x*cos(e^x)', '']
chain['sin(2^x)'] = ['ln(2)*2^x*cos(2^x)', '']
if options[0] == '1' and options[1] == '1' and type2 == 1:
# trig(poly)
chain['sin(x+1/x)'] = ['-cos(x + 1/x)*(1/x^2 - 1)', '']
chain['sin(x^2)'] = ['2*x*2)', '']
chain['sin(x^(1/2))'] = ['-1/(2*x^(1/2)*cos(x^(1/2)', '']
chain['sin(x^3+x)'] = ['(3*x^2+1)*cos(x^3+x)', '']
chain['sin(x^4)'] = ['4*x^3*cos(x^4)', '']
chain['cos(x^2)'] = ['-2*x*sin(x^2)', '']
chain['cos(x^3)'] = ['-3*x^2*sin(x^3)', '']
chain['cos(x^4+1/x)'] = ['-(4*x^3-1/x^2)*sin(x^4+1/x)', '']
chain['tan(x+1)'] = ['sec(x+1)^2', '']
chain['sec(x^(1/2))'] = ['1/(2*x^(1/2))*sec(x^(1/2))*tan(x^(1/2))', '']
chain['csc(1-x^2)'] = ['2*x*csc(1-x^2)*cot(1-x^2)', '']
chain['cot(3*x^3)'] = ['-9*x^2*csc(3*x^3)^2', '']
# poly(trig)
chain['sin(x)^2'] = ['2*x*cos(x^2)', '']
if (int(options[0:3]) == 111) and type2 == 1:
# trig(trig+ln, trig+poly, ln+poly)
chain['sin(ln(x)+x^2)'] = ['(1/x+2*x)*cos(ln(x)+x^2)', '']
# ln(trig+ln, trig+poly, ln+poly)
chain['ln(sin(x)+x)'] = ['(cos(x)+1)/(sin(x)+x)', '']
# poly(trig+ln, trig+poly, ln+poly)
chain['(3*sin(x)+ln(x))^2'] = ['2*(3*cos(x)+1/x)*(3*sin(x)+ln(x))', '']
# trig(poly(poly))
chain['sin((3*x-2)^2)'] = ['2*(3*x-2)*cos((3*x-2)^2)', '']
chain['sin((2*x+7)^3)'] = ['3*(2*x+7)^2*cos((2*x+7)^3)', '']
# ln(poly(poly))
chain['ln((3-2*x)^2)'] = ['(8*x - 12)/(2*x - 3)^2', '']
chain['ln(3-2*x)^2'] = ['(4*ln(3 - 2*x))/(2*x - 3)', '']
# 3 same
chain['ln(ln(ln(x)))'] = ['1/(x*ln(ln(x))*ln(x))', '']
chain['e^(e^(e^x))'] = ['e^x*e^(e^x)*e^(e^(e^x))', '']
chain['sin(sin(sin(x)))'] = ['cos(x)*cos(sin(x))*cos(sin(sin(x)))', '']
if options[3] == '1' and type2 == 1:
chain['sinh(cosh(x))'] = ['cosh(cosh(x))*sinh(x)', '']
chain['cosh(sinh(x))'] = ['sinh(sinh(x))*cosh(x)', '']
chain['sinh(sinh(x))'] = ['cosh(sinh(x))*cosh(x)', '']
chain['cosh(cosh(x))'] = ['sinh(cosh(x))*sinh(x)', '']
master_bank.update(chain)
product = {}
if type1 == 2 and type2 == 2:
# if options[2]=='1' and options[6]=='1':
# ln*ln
product['ln(x)*ln(2*x)'] = ['(ln(x)+ln(2*x))/x', '']
product['ln(x^3+1)*ln(2*x)'] = [
'ln(x^3+1)/x+(3*x^2*ln(2*x))/(x^3+1)', ''
]
product['ln(3*x)*e^(2*x^3)'] = ['e^(2*x^3)*(6*x^2*ln(3*x)+1/x)', '']
product['e^x*ln(2*x)'] = ['(ln(2*x)+1/x)*e^x', '']
if type1 == 0 and type2 == 2:
# if options[0]=='1' and options[6]=='1':
# poly*poly
product['(3*x^7+5*x^2)*(x^2+6*x^3)'] = [
'180*x^9+27*x^8+150*x^4+20*x^3', ''
]
product['(x+1)*(x^4+5*x)'] = ['5*x^4+4*x^3+10*x+5', '']
product['(2*x^2+1)*(5*x^3+1)'] = ['50*x^4 + 15*x^2 + 4*x', '']
product['(1-x^2)*(2*x^5-1)'] = ['-14*x^6+10*x^4+2*x', '']
product['(2*x^2-3*x+1)*(5*x^2-4*x)'] = ['40*x^3-69*x^2+34*x-4', '']
product['(3*x^2+1)*(x+7)'] = ['9*x^2+42*x+1', '']
product['(3*x^5+4)*(x^10-5*x^2)'] = [
'-15*x^4*(5*x^2-x^10)-(10*x-10*x^9)*(3*x^5+4)', ''
]
product['(x+1)*(x-1)'] = ['2*x', '']
if type1 == 1 and type2 == 2:
# if options[1]=='1' and options[6]=='1':
# trig*trig
product['sin(x)*cos(x)'] = ['cos(x)^2 - sin(x)^2', '']
product['sin(x)*tan(x)'] = ['cos(x)*tan(x) + sin(x)*(sec(x)^2)', '']
product['sin(x)*sec(x)'] = ['tan(x)', '']
product['sin(x)*csc(x)'] = ['0', '']
product['sin(x)*cot(x)'] = ['-sin(x)', '']
product['cos(x)*tan(x)'] = ['cos(x)', '']
product['cos(x)*sec(x)'] = ['0', '']
product['cos(x)*csc(x)'] = ['tan(x)', '']
product['cos(x)*cot(x)'] = ['-cos(x)*(2+cot(x)^2)', '']
product['tan(x)*sec(x)'] = ['-(cos(x)^2 - 2)/cos(x)^3', '']
product['tan(x)*csc(x)'] = ['sin(x)/cos(x)^2', '']
product['tan(x)*cot(x)'] = ['0', '']
product['sec(x)*csc(x)'] = ['1/cos(x)^2 - 1/sin(x)^2', '']
product['sec(x)*cot(x)'] = ['-cos(x)/sin(x)^2', '']
product['csc(x)*cot(x)'] = ['(sin(x)^2 - 2)/sin(x)^3', '']
if options[0] == '1' and options[1] == '1' and type2 == 2:
# if options[0]=='1' and options[1]=='1' and options[6]=='1':
# trig*poly
product['x*sin(x)'] = ['x*cos(x)+sin(x)', '']
product['x^2*sin(x)'] = ['x^2*cos(x)+2*x*sin(x)', '']
product['x*cos(x)'] = ['cos(x)-x*sin(x)', '']
product['x^2*cos(x)'] = ['2*x*cos(x)-x^2*sin(x)', '']
product['x*tan(x)'] = ['tan(x)+sec(x)^2', '']
product['x*sec(x)'] = ['sec(x)+x*sec(x)*tan(x)', '']
product['x*csc(x)'] = ['csc(x)-x*csc(x)*cot(x)', '']
product['x*cot(x)'] = ['cot(x)-x*csc(x)^2', '']
if options[1] == '1' and options[2] == '1' and type2 == 2:
# ln*trig
product['ln(x)*sin(x)'] = ['ln(x)*cos(x)+sin(x)/x', '']
product['ln(x)*cos(x)'] = ['-ln(x)*sin(x)+cos(x)/x', '']
product['e^x*sin(x)'] = ['e^x*(sin(x)+cos(x))', '']
product['e^x*cos(x)'] = ['e^x*(-sin(x)+cos(x))', '']
if options[0] == '1' and options[2] == '1' and type2 == 2:
# poly*ln
product['x*ln(x)'] = ['ln(x)+1', '']
product['x^2*ln(x)'] = ['2*x*ln(x)+x', '']
product['x^3*ln(x)'] = ['3*x^2*ln(x)+x^2', '']
product['x*e^x'] = ['(x+1)*e^x', '']
product['x^2*e^x'] = ['(x^2+2*x)*e^x', '']
product['x^3*e^x'] = ['(x^3+3*x^2)*e^x', '']
# poly^3
# trig^3
# ln^3
# ln^2* poly or trig
# poly^2*trig or ln
# trig^2* ln or poly
if options[0] == '1' and options[1] == '1' and options[
2] == '1' and type2 == 2:
# poly*trig*ln
product['(x+1)*ln(x)*sin(x)'] = [
'ln(x)*sin(x)+cos(x)*ln(x)*(x+1)+(sin(x)*(x+1))/x', ''
]
if options[3] == '1' and type2 == 2:
product['sinh(x)*cosh(x)'] = ['cosh(x)^2+sinh(x)^2', '']
product['sinh(x)*(sinh(x)^2+cosh(x))'] = [
'sinh(x)*(sinh(x) + 2*cosh(x)*sinh(x)) + cosh(x)*(sinh(x)^2 + cosh(x))',
''
]
product['cosh(x)*(sinh(x)+2)'] = ['cosh(x)^2+sinh(x)^2+2*sinh(x)', '']
quotient = {}
if type1 == 2 and type2 == 2:
# if options[2]=='1' and options[6]=='1':
# ln*ln
quotient['\displaystyle\\frac{ln(x)}{ln(2*x)}'] = [
'ln(2)', '(x*ln(2*x)^2)', ''
]
quotient['\displaystyle\\frac{ln(x^3+1)}{ln(3*x)}'] = [
'((3*x^2*ln(3*x))/(x^3 - 1) - ln(x^3 - 1)/x)', '(ln(3*x)^2)', ''
]
# quotient['\displaystyle\\frac{ln(3*x)*e^(2*x^3)}']=['exp(2*x^3)*(6*x^2*ln(3*x)+1/x)','']
# quotient['\displaystyle\\frac{e^x*ln(2*x)}']=['(ln(2*x)+1/x)*e^x','']
if type1 == 0 and type2 == 2:
# if options[0]=='1' and options[6]=='1':
# poly*poly
quotient['\displaystyle\\frac{7*x^4 + x^3 - 3}{x^2 - 1}'] = [
'(x^2 - 1)*(28*x^3 + 3*x^2) - 2*x*(7*x^4 + x^3 - 3)',
'(x^2 - 1)^2', ''
]
quotient['\displaystyle\\frac{x^2 + x}{x - 1}'] = [
'(2*x + 1)*(x - 1) - x - x^2', '(x - 1)^2', ''
]
quotient['\displaystyle\\frac{x}{x^2 - 1/x}'] = [
'x^2 - 1/x - x*(2*x + 1/x^2)', '(1/x - x^2)^2', ''
]
quotient['\displaystyle\\frac{x + 3}{1 - x}'] = ['4', '(x - 1)^2', '']
quotient['\displaystyle\\frac{x^4 + 2*x + 1}{1 - x^3}'] = [
'3*x^2*(x^4 + 2*x + 1) - (x^3 - 1)*(4*x^3 + 2)', '(x^3 - 1)^2', ''
]
quotient['\displaystyle\\frac{x^2 + 2*x + 1}{x + 3}'] = [
'(2*x + 2)*(x + 3) - 2*x - x^2 - 1', '(x + 3)^2', ''
]
if type1 == 1 and type2 == 2:
# if options[1]=='1' and options[6]=='1':
# trig*trig
quotient['\displaystyle\\frac{cos(x)}{sin(x) - 1}'] = [
'- cos(x)^2 - sin(x)*(sin(x) - 1)', '(sin(x) - 1)^2', ''
]
quotient['\displaystyle\\frac{sin(x)}{sin(x) + 1}'] = [
'cos(x)*(sin(x) + 1) - cos(x)*sin(x)', '(sin(x) + 1)^2', ''
]
quotient['\displaystyle\\frac{tan(x)}{sin(x) - cos(x)}'] = [
'- tan(x)*(cos(x) + sin(x)) - (cos(x) - sin(x))*(tan(x)^2 + 1)',
'(cos(x) - sin(x))^2', ''
]
quotient['\displaystyle\\frac{sin(x) - cos(x)}{cos(x) + sin(x)}'] = [
'2', '(cos(x) + sin(x))^2', ''
]
if options[0] == '1' and options[1] == '1' and type2 == 2:
# if options[0]=='1' and options[1]=='1' and options[6]=='1':
# trig*poly
quotient['\displaystyle\\frac{sin(x)}{x}'] = [
'x*cos(x) - sin(x)', 'x^2', ''
]
quotient['\displaystyle\\frac{tan(x)}{x}'] = [
'x*sec(x)^2 - tan(x)', 'x^2', ''
]
quotient['\displaystyle\\frac{cos(x)}{x^2 + 3}'] = [
'- sin(x)*(x^2 + 3) - 2*x*cos(x)', '(x^2 + 3)^2', ''
]
quotient['\displaystyle\\frac{x + sin(x)}{x^2 - 1}'] = [
'(x^2 - 1)*(cos(x) + 1) - 2*x*(x + sin(x))', '(x^2 - 1)^2', ''
]
quotient['\displaystyle\\frac{x - cos(x)}{x^2 + x}'] = [
'(sin(x) + 1)*(x^2 + x) - (x - cos(x))*(2*x + 1)', '(x^2 + x)^2',
''
]
quotient['\displaystyle\\frac{x}{sin(x)}'] = [
'sin(x) - x*cos(x)', 'sin(x)^2', ''
]
quotient['\displaystyle\\frac{x}{x + cos(x)}'] = [
'x + cos(x) + x*(sin(x) - 1)', '(x + cos(x))^2', ''
]
# quotient['\displaystyle\\frac{x^2 }{tan(x) - x^3}']=['2*x*(tan(x) - x^3) - x^2*(- 3*x^2 + tan(x)^2 + 1)','(tan(x) - x^3)^2','']
if options[1] == '1' and options[2] == '1' and type2 == 2:
# ln*trig
quotient['\displaystyle\\frac{sin(x)}{e^(x) - 1}'] = [
'cos(x)*(e^(x) - 1) - e^(x)*sin(x)', '(e^(x) - 1)^2', ''
]
quotient['\displaystyle\\frac{tan(x)}{ln(x)}'] = [
'ln(x)*(tan(x)^2 + 1) - tan(x)/x', 'ln(x)^2', ''
]
quotient['\displaystyle\\frac{sin(x) + tan(x)}{e^x+ln(x)}'] = [
'(e^x + ln(x))*(sec(x)^2 + cos(x))-(e^x + 1/x)*(sin(x)+tan(x))',
'(e^x + ln(x))^2', ''
]
quotient['\displaystyle\\frac{ln(x)}{cos(x)}'] = [
'cos(x)/x + ln(x)*sin(x)', 'cos(x)^2', ''
]
quotient['\displaystyle\\frac{cos(x) + e^(x)}{ln(x)}'] = [
'ln(x)*(e^(x) - sin(x)) - (cos(x) + e^(x))/x', 'ln(x)^2', ''
]
if options[0] == '1' and options[2] == '1' and type2 == 2:
# poly*ln
quotient['\displaystyle\\frac{ln(x)}{x}'] = ['1 - ln(x)', 'x^2', '']
quotient['\displaystyle\\frac{ln(x)}{x^2 + 1}'] = [
'(x^2 + 1)/x - 2*x*ln(x)', '(x^2 + 1)^2', ''
]
quotient['\displaystyle\\frac{x}{e^(x) + 1}'] = [
'e^(x) - x*e^(x) + 1', '(e^(x) + 1)^2', ''
]
quotient['\displaystyle\\frac{ln(x)}{e^(x) + ln(x)}'] = [
'(e^(x) + ln(x))/x - ln(x)*(e^(x) + 1/x)', '(e^(x) + ln(x))^2', ''
]
# poly^3
# trig^3
# ln^3
# ln^2* poly or trig
# poly^2*trig or ln
if options[3] == '1' and type2 == 2:
product['sinh(x)*cosh(x)'] = ['cosh(x)^2+sinh(x)^2', '']
product['sinh(x)*(sinh(x)^2+cosh(x))'] = [
'sinh(x)*(sinh(x) + 2*cosh(x)*sinh(x)) + cosh(x)*(sinh(x)^2 + cosh(x))',
''
]
product['cosh(x)*(sinh(x)+2)'] = ['cosh(x)^2+sinh(x)^2+2*sinh(x)', '']
master_bank.update(quotient)
master_bank.update(product)
# implicit={}
if type2 == 3:
if int(options[0:3]) == 111:
implicit = partial.partial(2, 'mixed')
else:
if type1 == 0: # poly
implicit = partial.partial(2, 'poly')
if type1 == 1: # trig
implicit = partial.partial(2, 'trig')
if type1 == 2: # trans
implicit = partial.partial(2, 'trans')
if type1 == 3: # hypinv
implicit = partial.partial(2, 'hypinv')
# master_bank.update(implicit)
# print len(master_bank)
if type2 != 3:
rand1 = random.randrange(0, len(master_bank))
f = master_bank.keys()[rand1]
if len(master_bank[f]) == 3:
ans = '(%s)/(%s)' % (master_bank[f][0], master_bank[f][1])
anstex = 'The answer is $f\'(x)=\displaystyle\\frac{%s}{%s}$' % (
toTEX(master_bank[f][0]), toTEX(master_bank[f][1]))
else:
ans = master_bank[f][0]
anstex = 'The answer is $f\'(x)=' + toTEX(ans) + '$'
probtex = 'Given the function $f(x)=' + toTEX(
f) + '$, find the derivative $f\'(x)$'
prefix = '$f\'(x)=$'
hint = ''
else:
f = implicit.f
ans = implicit.yx
hint = ''
probtex = 'Given the equation $' + frac(toTEX(f)) + '=0$, find $y\'.$'
prefix = '$y\'=$'
anstex = 'The answer is $y\'=' + frac(toTEX(ans)) + '$'
suffix = ''
if type2 == 1:
hint = 'Use <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/chainrule" target="_blank">Chain Rule</a>.'
elif type2 == 2 and len(master_bank[f]) == 3:
hint = 'Use <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/productrule" target="_blank">Product Rule or the Quotient Rule</a>.'
elif type2 == 2 and len(master_bank[f]) < 3:
hint = 'Use <a class="hintlink" href="http://www.calcta.com/tutorial.php?page=derivative/productrule" target="_blank">Product Rule</a>.'
print probtex
print ans
print anstex
print prefix
print suffix
print hint
def test_with_many_arguments(self):
template = "{0} {1} and {2} and {red} {green} and {blue}"
with_four_args = partial(template.format, 1, 2, 3, 4)
with_kwargs_too = partial(with_four_args, red=4, green=5, blue=6)
self.assertEqual(with_kwargs_too(), "1 2 and 3 and 4 5 and 6")
def register(self, entry_name, constructor, *args, **kargs):
''' register a constructor '''
if self.is_registered(entry_name):
raise ValueError('Duplicate %s' % entry_name)
self.registered[entry_name] = partial(constructor, *args, **kargs)
def register(self, methodName, constructor, *args, **kargs):
''' register a constructor '''
if self.is_registered(methodName):
raise ValueError(methodName)
setattr(self, methodName, partial(constructor, *args, **kargs))
def register(self, entry_name, constructor, *args, **kargs):
''' register a constructor '''
if self.is_registered(entry_name):
raise ValueError( 'Duplicate %s' % entry_name )
self.registered[entry_name] = partial(constructor, *args, **kargs)
def register(self, methodName, constructor, *args, **kargs):
''' register a constructor '''
if self.is_registered(methodName):
raise ValueError( methodName )
setattr(self, methodName, partial(constructor, *args, **kargs) )
