# Calculating the Derivative at a Specific Point Using Python

To compute the derivative of a mathematical function f(x) at a specific point using Python, one can utilize the derivative() function from the misc module of scipy.

from scipy import misc
def f(x):
...
misc.derivative(f,x0)

• The first argument, f, represents the function for which the derivative is to be calculated.
• The second argument, x0, denotes the point at which the derivative is evaluated.

The derivative() function determines the first derivative of f(x) at the specified point x0.

So, what exactly is the derivative at a point? It represents the value of the derivative f '(x) when x = x0.

## Examples

Example 1

Consider the function f(x)=x2

$$f(x) = x^2$$

To determine the derivative of f(x) at the point x = 4:

>>> from scipy import misc
>>> def f(x):
return x*x
>>> misc.derivative(f,4)

The derivative() function computes the value of the first derivative f'(x) at x = 4.

The resulting value is 8.0, implying that the first derivative of f(x) at x = 4 is 8.

8.0

Verification:

Example 2

For this example, we'll define a slightly more intricate function g(x) = 4x2 + 3x + 2.

$$g(x) = 4x^2 + 3x + 2$$

To compute the derivative of g(x) at x = 3:

>>> from scipy import misc
>>> def g(x):
return 4*x**2+3*x+2
>>> misc.derivative(g,3)

The computed value is 27.0, signifying that the first derivative of g(x) at x = 3 is 27.

27.0

Verification

https://how.okpedia.org/en/python/find-the-derivative-at-a-point-with-python

Report us an error or send a suggestion to improve this page

Python Derivative