Hi, I’m Differentiation.

Complex? Me? Not at all. I’m more simpler than you would ever think.

Superhero Minion (I’m Differentiation)

Hi everyone… Welcome to my showcase.

I have always been wondering, why people feel complex, whenever they hear my name “The Differentiation❕ ”. You would find me funny, as you continue spending time with me. Come on..Let’s have a discussion.

Introduction

I am a part of my parent “Calculus”. Yes, it combines a lot of my siblings including me. All of us were introduced to this world, by many brain storming people whom you call “Mathematicians”. A gentle thanks to all of those who struggled hard to introduce us, to this world.

What do I do?

Just like all of you, I work a lot. I work continuously, day and night, sun and moon, just to quantify(calculate) the rate of change in “something” because of changes occurring in “something else”. To be more formal and mathematical, I work on finding out, the derivative of a given function f(x).

What! The rate of Change in something….something else?

Wait, let me clear your confusion with a simple example.

Let’s say, you have a GYM freak friend ( Why GYM Freak ? Because, I have got one). You may have observed him, taking good diet and doing different types of workouts, to keep his body in perfect shape. What if, he stops his diet and workout? He would gradually loose his shape. But, How gradually? In how many days? What is the rate of change in his body’s shape because of the change in his diet and workout? These are the questions, I always try to answer.

The above one is just an example. I can’t really say, what’s the rate of change in his body, with his diet and workout plan? Since the only language I know is, “Mathematics”, I need, the “change” to be expressed as a mathematical function. Just like the following…

Everything happening in this nature, can always be expressed as mathematical function — by Pavan Kumar Yekabote.

Expressing the change as a function:

Let’s say, we are able to numerize the diet plan and work out.

• Diet plan and work out = x
• Body’s shape = y

Now, let a function f (x) takes our input x, undergoes some calculations with x to produce, y. Therefore, y= f ( x ) is the function, we could form. Now let’s say, f ( x ) = 3x + 2, which means y = f(x) = 3x + 2.

So, if

• x = 3, then y = f( 3 ) = ( 3 * 3 ) + 2 = 11, therefore (x1, y1) = ( 3, 11 )
• x = 5, then y = f( 5 ) = (3 * 5) + 2 = 17, therefore (x2, y2) = ( 5, 17)

Is this it? Is this, what I do? Why are we applying the function f(x) for two values i.e, 3 and 5? We are taking two values because, when we are speaking about change, we need at least two values to compare in between. And no, we are not yet done. Here comes the most important part of my job, and this is how I’m recognized. It’s time, we apply me on the given function f(x).

When I am applied on

• A function f(x) [ f of x ], the function looks like f’(x) [ f dash of x ]
• An expression where y changes based on changes occurring in x, then the expression looks like d y / d x

Let’s apply me on our function f(x) = 3x + 2 values. Now, the function looks like

Fig 1. Expressing function f(x) after applying differentiation.

Here is the change function. Since we have seen from the above image, how I can find out the changes, let us see what is the change in shape of body, because of change occurring in the diet and the work out plan.

From the calculations :

• ( old diet & workout , old shape of body ) = ( x1, y1 ) = ( 3, 11)
• ( New diet & workout , New shape of body ) = ( x2, y2 ) = ( 5, 17 )

Fig 2 : Calculating the change from given two points.

Therefore, the rate of change in body’s shape, because of change in diet and workout plan, for given function f(x) is, 3. Which means, the body’s shape is changing constantly, at a rate of 3 units with respect to diet & workout.

Another classic example can be, Speed, which is the rate of change of distance with change in time.

That’s all. Finally, This is me. “ The Differentiation”. Now I hope, you won’t fear /feel complex when you hear me. This is what, I always try to do.

Till now, you have understood how I calculate the rate of change using given two points of function.There are situations where I don’t actually get points, but just the expression itself. At those situations,How do I actually calculate the rate of change ? Those are going to be discussed in the next article.

Thank you for spending your time with me. I hope you had great fun. Signing off…

Yours…,
Differentiation.

Find out this interesting article on Neural networks in the following link.

Neural Networks from scratch — Perceptron Approach