def test_7():
'''
Testing x**2/sqrt(x) + arccos(x) derivative and value
This also tests division and power overrides
'''
v = 4
x = AD.AADVariable(v)
x = x**2 / AD.sqrt(x)
#value check
assert abs(x.val - v**2 / math.sqrt(v)) < tol
#derivative check
assert abs(x.der - (3. * math.sqrt(v)) / 2.) < tol
def test_6():
'''
Testing sqrt(x)*arctan(x) + arccos(x) derivative and value
This also tests multiplication operator overides
'''
v = 0.5
x = AD.AADVariable((v))
x = AD.sqrt(x) * AD.arctan(x) + AD.arccos(x)
#value check
assert abs(x.val - (math.sqrt(v) * math.atan(v) + math.acos(v))) < tol
#derivative check
assert abs(x.der - (math.sqrt(v) / (v**2 + 1.) - 1. /
(math.sqrt(1. - v**2)) + (math.atan(v) /
(2. * math.sqrt(v))))) < tol