#!/usr/bin/env python
# coding: utf-8

# ## Exercise for the course [Python for MATLAB users](http://sese.nu/python-for-matlab-users-ht15/), by Olivier Verdier

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get_ipython().run_line_magic('pylab', '')
get_ipython().run_line_magic('matplotlib', 'inline')


# A numerical derivative of a function $f$ is a formula of the type
# \\[
# f'(x_0) \simeq \frac{f(x_0+h/2) - f(x_0-h/2)}{h}
# \\]

# Implement a function `derivator` which returns the derivative *function*.

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def derivator(f, h):
    pass


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msin_ = derivator(cos, 1e-10)


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assert(allclose(msin_(0), 0))
assert(allclose(msin_(pi), 0))
assert(allclose(msin_(pi/2), -1.))