def test_diff():
x, y = symbols('x, y')
assert Rational(1, 3).diff(x) is S.Zero
assert I.diff(x) is S.Zero
assert pi.diff(x) is S.Zero
assert x.diff(x, 0) == x
assert (x**2).diff(x, 2, x) == 0
assert (x**2).diff(x, y, 0) == 2 * x
assert (x**2).diff(x, y) == 0
pytest.raises(ValueError, lambda: x.diff(1, x))
a = Symbol("a")
b = Symbol("b")
c = Symbol("c")
p = Rational(5)
e = a * b + b**p
assert e.diff(a) == b
assert e.diff(b) == a + 5 * b**4
assert e.diff(b).diff(a) == Rational(1)
e = a * (b + c)
assert e.diff(a) == b + c
assert e.diff(b) == a
assert e.diff(b).diff(a) == Rational(1)
e = c**p
assert e.diff(c, 6) == Rational(0)
assert e.diff(c, 5) == Rational(120)
e = c**Rational(2)
assert e.diff(c) == 2 * c
e = a * b * c
assert e.diff(c) == a * b
def test_diff():
x, y = symbols('x, y')
assert Rational(1, 3).diff(x) is Integer(0)
assert I.diff(x) is Integer(0)
assert pi.diff(x) is Integer(0)
assert x.diff(x, 0) == x
assert (x**2).diff(x, 2, x) == 0
assert (x**2).diff(x, y, 0) == 2*x
assert (x**2).diff(x, y) == 0
pytest.raises(ValueError, lambda: x.diff(1, x))
a = Symbol("a")
b = Symbol("b")
c = Symbol("c")
p = Integer(5)
e = a*b + b**p
assert e.diff(a) == b
assert e.diff(b) == a + 5*b**4
assert e.diff(b).diff(a) == 1
e = a*(b + c)
assert e.diff(a) == b + c
assert e.diff(b) == a
assert e.diff(b).diff(a) == 1
e = c**p
assert e.diff(c, 6) == 0
assert e.diff(c, 5) == 120
e = c**2
assert e.diff(c) == 2*c
e = a*b*c
assert e.diff(c) == a*b
f = Function('f')
assert f(x).diff(x, 2).diff(f(x).diff(x, 1)) == 0
def test_diff():
x, y = symbols('x, y')
assert Rational(1, 3).diff(x) is Integer(0)
assert I.diff(x) is Integer(0)
assert pi.diff(x) is Integer(0)
assert x.diff(x, 0) == x
assert (x**2).diff(x, 2, x) == 0
assert (x**2).diff(x, y, 0) == 2*x
assert (x**2).diff(x, y) == 0
pytest.raises(ValueError, lambda: x.diff(1, x))
a = Symbol('a')
b = Symbol('b')
c = Symbol('c')
p = Integer(5)
e = a*b + b**p
assert e.diff(a) == b
assert e.diff(b) == a + 5*b**4
assert e.diff(b).diff(a) == 1
e = a*(b + c)
assert e.diff(a) == b + c
assert e.diff(b) == a
assert e.diff(b).diff(a) == 1
e = c**p
assert e.diff(c, 6) == 0
assert e.diff(c, 5) == 120
e = c**2
assert e.diff(c) == 2*c
e = a*b*c
assert e.diff(c) == a*b
f = Function('f')
assert f(x).diff(x, 2).diff(f(x).diff(x, 1)) == 0
def test_diff():
assert Rational(1, 3).diff(x) is Integer(0)
assert I.diff(x) is Integer(0)
assert pi.diff(x) is Integer(0)
assert x.diff((x, 0)) == x
assert (x**2).diff((x, 2), x) == 0
assert (x**2).diff(x, (y, 0)) == 2*x
assert (x**2).diff(x, y) == 0
pytest.raises(ValueError, lambda: x.diff((1, x)))
p = Integer(5)
e = a*b + b**p
assert e.diff(a) == b
assert e.diff(b) == a + 5*b**4
assert e.diff(b).diff(a) == 1
e = a*(b + c)
assert e.diff(a) == b + c
assert e.diff(b) == a
assert e.diff(b).diff(a) == 1
e = c**p
assert e.diff((c, 6)) == 0
assert e.diff((c, 5)) == 120
e = c**2
assert e.diff(c) == 2*c
e = a*b*c
assert e.diff(c) == a*b
f = Function('f')
assert f(x).diff((x, 2)).diff(f(x).diff((x, 1))) == 0