Maths and AI | Calculus-1 | Importance of calculus in Machine Learning

Calculus is one of most important parameter in calculus. In this article I will explain briefly about calculus.Here I am assuming that you have some basic idea of derivatives.

What is derivative and how to calculate derivative of a function f(x)?

The derivative of a function of a real variable measures the sensitivity to change of the output value with respect to a change in its input value.

Derivative of f(x)

Let’s take an example to calculate derivative:

f(x) = 3x+9

We want to know what is the rate of change of f(x) with small change in x. To calculate this we will find its derivative.

derivative of f(x) = f’(x) = 3

So we can conclude from our calculation that in above function, rate of change of f(x) with respect to x will be constant.

What is chain rule?

So in above example our f(x) was 3x+9 and we simply want to find its rate change with respect to x. Now how will we calculate rate of change of new function g(x) = sin(f(x)). We can rewrite g(x) = sin(3x+9) . Can you find the rate of change of g(x) with respect to x. To differentiate this you have to follow some steps:

1. First differentiate Sin(f(x)) with respect to x which is Cos(f(x)).

2. Now differentiate f(x) with respect to x which is 3.

3. multiply both differentiations which will be your final answer.

differentiation of g(x) = cos(f(x))*f’(x) = 3cos(3x+9)

Advance rules of derivatives (chain rule) which we will use in machine learning.

suppose y = sin(t) ; t = exp(k) ; k = 3x+9

You have to find dy/dx . How will you calculate this?

dy/dx calculation

This is how you can compute any differentiation of a function. This formula is widely used in deep learning. Do better practice of this rule to understand deep learning.

https://quickmath.com/webMathematica3/quickmath/calculus/differentiate/basic.jsp article

Here is one of the article which i personally like the most about differentiation.(optional read: — https://medium.com/analytics-vidhya/unraveling-automatic-differentiation-6d5f0196f219)

If you understand chain rule and basics of differentiation then you are almost ready to learn machine learning algorithms. Before starting machine learning i will briefly explain the python programming language so that you can write your program and test it.

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