def print_Chain(self, rule):
with self.new_step(), self.new_u_vars() as (u, du):
self.append("Sea {}.".format(self.format_math(sympy.Eq(u, rule.inner))))
self.print_rule(replace_u_var(rule.substep, rule.u_var, u))
with self.new_step():
if isinstance(rule.innerstep, FunctionRule):
self.append(
"Entonces, aplicando la regla de la cadena. Multipicamos por {}:".format(
self.format_math(
sympy.Derivative(rule.inner, rule.symbol))))
self.append(self.format_math_display(diff(rule)))
else:
self.append(
"Entonces, aplicando la regla de la cadena. Multipicamos por {}:".format(
self.format_math(
sympy.Derivative(rule.inner, rule.symbol))))
with self.new_level():
self.print_rule(rule.innerstep)
self.append("El resultado de la regla de la cadena:")
self.append(self.format_math_display(diff(rule)))
def print_Chain(self, rule):
with self.new_step(), self.new_u_vars() as (u, du):
self.append("Let {}.".format(self.format_math(sympy.Eq(u, rule.inner))))
self.print_rule(replace_u_var(rule.substep, rule.u_var, u))
with self.new_step():
if isinstance(rule.innerstep, FunctionRule):
self.append(
"Then, apply the chain rule. Multiply by {}:".format(
self.format_math(
sympy.Derivative(rule.inner, rule.symbol))))
self.append(self.format_math_display(diff(rule)))
else:
self.append(
"Then, apply the chain rule. Multiply by {}:".format(
self.format_math(
sympy.Derivative(rule.inner, rule.symbol))))
with self.new_level():
self.print_rule(rule.innerstep)
self.append("The result of the chain rule is:")
self.append(self.format_math_display(diff(rule)))
def print_Chain(self, rule):
with self.new_step(), self.new_u_vars() as (u, du):
self.append("Let {}.".format(
self.format_math(sympy.Eq(u, rule.inner))))
self.print_rule(replace_u_var(rule.substep, rule.u_var, u))
with self.new_step():
if isinstance(rule.innerstep, FunctionRule):
self.append(
"Then, apply the chain rule. Multiply by {}:".format(
self.format_math(
sympy.Derivative(rule.inner, rule.symbol))))
self.append(self.format_math_display(diff(rule)))
else:
self.append(
"Then, apply the chain rule. Multiply by {}:".format(
self.format_math(
sympy.Derivative(rule.inner, rule.symbol))))
with self.new_level():
self.print_rule(rule.innerstep)
self.append("The result of the chain rule is:")
self.append(self.format_math_display(diff(rule)))
def print_U(self, rule):
with self.new_step(), self.new_u_vars() as (u, du):
# commutative always puts the symbol at the end when printed
dx = sympy.Symbol("d" + rule.symbol.name, commutative=0)
self.append("Let {}.".format(self.format_math(sympy.Eq(u, rule.u_func))))
self.append(
"Then let {} and substitute {}:".format(
self.format_math(sympy.Eq(du, rule.u_func.diff(rule.symbol) * dx)),
self.format_math(rule.constant * du),
)
)
integrand = rule.substep.context.subs(rule.u_var, u)
self.append(self.format_math_display(sympy.Integral(integrand, u)))
with self.new_level():
self.print_rule(replace_u_var(rule.substep, rule.u_var, u))
self.append("Now substitute {} back in:".format(self.format_math(u)))
self.append(self.format_math_display(_manualintegrate(rule)))
def print_U(self, rule):
with self.new_step(), self.new_u_vars() as (u, du):
# commutative always puts the symbol at the end when printed
dx = sympy.Symbol('d' + rule.symbol.name, commutative=0)
self.append("Let {}.".format(
self.format_math(sympy.Eq(u, rule.u_func))))
self.append("Then let {} and substitute {}:".format(
self.format_math(
sympy.Eq(du,
rule.u_func.diff(rule.symbol) * dx)),
self.format_math(rule.constant * du)))
integrand = rule.substep.context.subs(rule.u_var, u)
self.append(self.format_math_display(sympy.Integral(integrand, u)))
with self.new_level():
self.print_rule(replace_u_var(rule.substep, rule.u_var, u))
self.append("Now substitute {} back in:".format(
self.format_math(u)))
self.append(self.format_math_display(_manualintegrate(rule)))
