# Differentiation by intuition

We all have been taught of differentiation.We all have been taught of different set of rules on how to differentiate a particular equation with respect to a variable . These rules acts as building blocks to solving differentiation on more complex equations.But we were never been taught on how to intuitive think on differentiation. I wanted to understand how by intuition we could solve and understand these building blocks. Lets start with simple example of what it means to differentiate.

Differentiation of an area of a circle .

Area of a circle of radius r is πr2

In simple terms differentiation is about how the area of the circle changes for a unit change in r.

Lets calculate the increase in the area of this change .

`new area = πr`2`+ area of the circle of thickness one unit.`

Area of the circle of thickness one unit

The area occupied by the line of shape circle of one unit thickness is basically the circumference of the circle .Hence ,
`additional area = 2πr` So ,

`new area = πr`2`+ 2πr`

So the change in area of circle per change in unit of r is 2πr .

And according to building blocks , Differentiation of area of circle is :

And yes , we derived the differentiation of circle by intuition.

We now by intuition are able to think about what a differentiation is doing to an equation. We will see more examples in the next blogs.

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