(Part — 1)What are derivatives and how to use them in Artificial Neural Networks?

From our school days, we heard something called Derivatives. Which sounds like a zombie.

Yeah, I know!!!!! Most of us must ever have this question why derivatives? What is the use of derivatives in real life? But guys believe me this is one of the interesting topics that is changing everyone’s world. I am writing this blog because I failed a lot of times in mathematics. I don’t want to let others suffer the same. In this blog, I am not going to teach how to find derivatives but I will teach you how it works and how to use them in real life.

Guys before starting the topic. I have simple question for you. What is 2+2 =?. It’s very easy it's 4. Now what if I ask how can you use this property in our daily life? It’s again very simple. We use a lot this property of addition in many areas. Like for transaction purposes in our daily life. In this blog first we will understand how derivative acts? Once you learned how derivative behaves then I will teach you how can you use this in your real life.

So let’s get started.

Suppose I have a simple equation f(a) = 3a, if we try to draw a graph then it will look like this.

Now how can we draw its graph? We simply input some values in the equation f(a) = 3a and then the output generated will be our graph.

Example: if a = 1 : output: 3

if a = 2 : output: 6

if a = 3 : output: 9

if a = 4 : output: 12

if we plot the 3,6,9,12 in a graph it will be looks like the above graph.

Now here are derivatives will be taught:

suppose for now if I will add a = 2 in our equation, then f(a) will be 6.

Let's do a little change in the value of a. For Example: from 2 to 2.001 which means 0.001

Then the output will be 6.003 which means there is a change of 0.003.

Let's make a small triangle inside these both lines as shown here in the image.

From our previous input and this triangle, we can easily judge that if we simply give a change of 0.001 on the right then it's going to bump up by 0.003. This is also known as a slope.

Whereas a slope is a height/width. So according to the previous input height is 0.003 and width is 0.001. so slope would be 0.003/0.001 = 3. Indirectly it’s showing if we add any input (0.001) to this equation

( f(a) = 3a ) then how much change (0.003) it's going to happen. This is being told by derivatives (slope).

If we add 2 then it's going to be 6 (3 times change)

If we add 2.001 it's going to be 2.003 (3 times change)

If we add 3 it's going to be 9 (3 times change)

If we try to find out slope for these three values then slope will be 3. It means derivatives is 3.

Summary : for the function f(a)= 3a the derivative would be 3. The process of finding the amount of change that is going to happen when any input is given to a particular function ( f(a) = 3a ) is known as derivatives.

Now we are aware of what is the behavior of derivatives. In the upcoming blogs, I will show you how can you use this behavior of derivatives to train the neural network model and create a human-like brain.