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 = πr2+ 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 = πr2+ 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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