How to Find the Derivative of a Function in Python

In this tutorial, we will learn how to calculate the derivative of a function using Python.

Derivatives are essential in various fields of mathematics, such as calculus and optimization. They give us insights into how a function behaves, how its input changes affect its output and much more.

We will explore two popular methods for calculating derivatives in Python: using the SymPy library and using Python numerical methods with the help of NumPy and SciPy libraries. Both methods have their own advantages, and the choice mainly depends on the type of problem you’re dealing with.

Step 1: Installing Required Libraries

Before we start, we need to install the required libraries. In this tutorial, we will be using the following libraries:

  1. SymPy
  2. NumPy
  3. SciPy

You can install these libraries using the following command:

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pip install sympy numpy scipy

Step 2: Calculating Derivative using SymPy

SymPy is a Python library for symbolic mathematics. It allows us to work with algebraic expressions in a clean and readable way. Follow the below steps to calculate the derivative of a function using SymPy:

  1. Import the library.
  2. Define the variables and function.
  3. Calculate the derivative.

Here is an example:

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from sympy import symbols, diff
 
x = symbols('x')
function = x**2 + 5*x + 6
 
derivative = diff(function, x)
print(derivative)

In this example, we calculate the derivative of the function: x^2 + 5x + 6. The output of the code will be:

2*x + 5

We get the derivative of the given function as 2x + 5.

Step 3: Calculating Derivative using Numerical Methods (NumPy and SciPy)

In some cases, when it’s difficult to get a symbolic solution for the derivative, we can use numerical methods. Here, we will use the NumPy and SciPy libraries to calculate the derivative of a function at a specific point using numerical methods.

The following steps demonstrate how to achieve this:

  1. Import the required libraries.
  2. Define the function.
  3. Calculate the derivative using numerical methods.

Here is an example:

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import numpy as np
from scipy.misc import derivative
 
def function(x):
    return x**2 + 5*x + 6
 
x_val = 3
derivative_val = derivative(function, x_val, dx=1e-6)
 
print(derivative_val)

In this example, we calculate the derivative of the same function as before (x^2 + 5x + 6) at the point x = 3. The output of the code will be:

11.000000000086097

We get the approximate derivative value as 11 at the point x = 3 for the given function.

Conclusion

In this tutorial, we learned how to calculate the derivative of a function using Python. We explored two popular methods: using the SymPy library for symbolic calculations and using the numerical method with the help of NumPy and SciPy libraries.

The choice between the two methods depends on the complexity of the function, and whether you need the symbolic representation of the derivative or an approximate value at specific points.