Polynomial derivates can be achieveed with the method polyder():
>>> np.polyder([2,1/3,2,1])
array([6, 0, 2])
>>> np.polyder([2, 1.0/3, 2, 1])
array([ 6. , 0.66666667, 2. ])
>>>
Integration with polyint():
>>> np.polyint([6.0,2.0/3,2.0])
array([ 2. , 0.33333333, 2. , 0. ])
>>>