Writing the Derivative Function

For all the fear whipped up about derivatives in calculus courses, the function for calculating a derivative numerically is surprisingly easy.

In a Jupyter notebook, we'll define a function, f(x), to be the parabola y = x2:

def f(x):
    return x**2

Now we can write a function to calculate the derivative at any point (x, f(x)) using the classic formula:

Figure 10.4: Formula for calculating derivatives

The numerator is the rise and the denominator is the run. Δ x means the change in x, and we're going to make that a really small decimal by dividing 1 by a million:

def f(x):
    return x**2
def derivative(f,x):
    """
    Returns the value of the derivative of
    the function at a given x-value.
    """
    delta_x = 1/1000000
 ...