How do I compute derivative using Numpy?

Question

How to compute the derivative of a function?

For example:

y=x^2+1

using NumPy?

Now, I need the value of the derivative at x=6..

Answer 1

Actually, You have 4 options

1. Finite Differences
2. Symbolic Differentiation
3. Automatic Derivatives 
4. Compute derivatives by hand

Look at the example using SymPy

In [1]: from sympy import *

In [2]: import numpy as np

In [3]: x = Symbol('x')

In [4]: y = x**2 + 1

In [5]: yprime = y.diff(x)

In [6]: yprime

Out[6]: 2⋅x

In [7]: f = lambdify(x, yprime, 'numpy')

In [8]: f(np.ones(5))

Out[8]: [ 2.  2.  2.  2.  2.]

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