
Without mathematics, there’s nothing you can do. Everything around you is mathematics. Everything around you is numbers. — Shakuntala Devi
Mathematics is a significant aspect of Machine Learning. While some may absolutely adore math, others may dislike it. However, it is essential to have at least some knowledge of math and understand the concepts of probability, statistics, and calculus to succeed in solving machine learning tasks.
In this article, we will focus on differential and integral calculus. These two concepts are vital aspects of learning machine learning concepts. While integral calculus might not find much utility at the start of your machine learning journey, it gains more significance when you gain further knowledge of the subject.
On the other hand, differential calculus and differentiation play a vital role in accomplishing many objectives of machine learning. One of the most important use cases of differentiation can be noticed in backpropagation through neural networks or other similar structures. To verify the results of the output or produce effective results during training, differentiation and backpropagation play a crucial role.
In this article, we will keep everything simple and easy. We will learn more about the sympy library which we will utilize for the simplification of differentiation and integration. We will finally build a simple differential calculator after understanding the basic concepts of this library. Without further ado, let us get started by exploring these topics.
What Is sympy?

We have discussed that integral and differential calculus are considered as a pre-requisite for understanding multiple machine learning concepts like backpropagation. Luckily, python also offers a free, lightweight, python-based library called sympy. It is a python library for symbolic Mathematics.
Before you install the sympy library on your system, there are a few pre-requisite requirements. One of the main requirements is that you need to have the mpmath Python library installed in your environment. The recommended method of installation is with the help of the Anaconda environment, as most of the pre-requisite requirements come installed here.
Anaconda is a free Python distribution from Continuum Analytics that includes SymPy, Matplotlib, IPython, NumPy, and many more useful packages for scientific computing. The following command should be used to update the Sympy library.
conda update sympy
For a normal installation, once you fulfill the requirements, including having a version of Python greater than 3.5, you can install this library with the following command.
pip install sympy
After the installation of this library, you can proceed to perform mathematical calculus operations like integration and differentiation in a few lines of code. Let us firstly experiment with some code blocks with both differentiation and integration. After learning some basic functionalities, we will proceed to build a simple differential calculator.
Differentiation Made Easy With Sympy:
In this section of the article, we will understand some of the basic functionalities and operations related to differentiation with sympy. Firstly, we will import the library, and then proceed to follow the steps to differentiate a specific function with ease. It is recommended that you follow along side by side on a Jupyter Notebook to achieve the best possible results on each code sample.
import sympy
We will proceed to analyze some basic functionalities and operations of the sympy library. Firstly, we need to define a variable for the type of symbol it will carry. Here ‘x’ is our symbol of choice. Once you have the symbol planned out, you can proceed to perform your differentiation operation. In the example, I have done a simple computation for the following function – 5x². You can feel free to experiment with the library and explore more.
x = sympy.Symbol('x')
deriv = sympy.diff(5*(x**2))
deriv
Result:
10𝑥
To understand all the required rules of differentiation for building more unique projects, I would recommend checking out the following link from here.
Integration Made Easy With Sympy:
In this section of the article, we will understand some of the basic functionalities and operations related to integration with sympy. Firstly, we will import the library, and then proceed to follow the steps to perform integration on a couple of functions. To understand all the required rules of integration for building more unique projects, I would recommend checking out the following link from here.
from sympy import *
In the next couple of code blocks, we will proceed to perform some basic operations for integration. These functions are quite simple and self-explanatory, with a basic understanding of integration.
x = Symbol('x')
limit(sin(x)/x, x, 0)
Result:
1
integrate(1/x, x)
log(x)
Result:
log(𝑥)
With this basic knowledge of sympy, let us proceed to build a simple project for a differential calculator in the next section of this article.
Simple Project:
Now, we will construct a simple project for a basic differential calculator. To understand all the required rules of differentiation for building this calculator, I would recommend checking out the following link from here. I will only provide a small code snippet on the type of differential calculator that I am trying to build. You can use your own innovative ideas and perform much more effective differential calculators. Below is a simple code block for a sample of a few of the possible functions for a Derivative Calculator.
class Derivative_Calculator:
def power_rule(*args):
deriv = sympy.diff(*args)
return deriv
def sum_rule(*args):
derive = sympy.diff(*args)
return deriv
I have made use of the Derivative Calculator class to write a bunch of functions with the *args comment as we don’t know the number of elements that will be passed through the function. This concept is useful for building the differential calculator. I have made use of only a few of these rules of differentiation. I would encourage the users to try out more of these. The below article is a guide to understand advanced functions in Python with codes and examples.
Understanding Advanced Functions In Python With Codes And Examples!
In the next code block, we will allow the user to pick an option on which they want to perform a specific operation. These option choices will range from the different types of differentiation rules. You can feel free to experiment and build a differential calculator of your preference.
print("""
Enter The Type of Operation to be Performed: (Choose the number of your choice -)
1. Power Rule
2. Sum or Difference Rule
3. Product Rule
4. Chain Rule
""")
Operation = int(input())
Derivative = input("Enter your derivative: ")
The following code block above will produce the below result. Here I choose by option as ‘1’ to activate the power rule, and perform a computation on the function 3x².
Result:
Enter The Type of Operation to be Performed: (Choose the number of your choice -)
1. Power Rule
2. Sum or Difference Rule
3. Product Rule
4. Chain Rule
1
Enter your derivative: 3*x**2
Finally, I will activate the code block below which will enable the working of my class and the power rule function to input the correct answer.
differentiatie = Derivative_Calculator
differentiatie.power_rule(Derivative)
Result:
6𝑥
As we can notice, the accurate answer after differentiation is provided. Albeit a simple project, I would encourage all of you to make it more complex and innovative!
Conclusion:

Pure mathematics is, in its way, the poetry of logical ideas. — Albert Einstein
The knowledge of mathematics is crucial for understanding the intricate details of machine learning and become an expert in the field. Only with a detailed understanding of math, you will be able to interpret some of the key concepts, which are required to go in-depth into particular topics. Most machine learning algorithms require math, and the study of calculus stands out as one of the essential elements to progress further in machine learning.
In this article, we learned about why mathematics is essential for any enthusiast pursuing machine learning. We then proceeded to understand the basic elements related to the sympy library and how it can be utilized for differential and integral calculus. Finally, we built a simple project of a derivative calculator, which can be improved to suit your purposes and utilize to simplify your real-life calculations.
You can check out the official documentation from here for further details on how to utilize this module. However, if you are still any confusions related to the topics discussed in this article, then please free to let me know. I will try to get back to you as soon as possible with a quick response.
Check out some of my other articles that you might enjoy reading!
5 Essential Skills To Develop As A Data Scientist!
5 NLP Topics And Projects You Should Know About!
AI In Chess: The Evolution of Artificial Intelligence In Chess Engines
7 Tips To Crack Data Science And Machine Learning Interviews!
Thank you all for sticking on till the end. I hope all of you enjoyed reading the article. Wish you all a wonderful day!