Chapter 2- Differentiation

Topic: Differentiation by first principal

Introduction to Derivatives

                                        It is all about slope!

                                                             

Slope  =

Change in Y Change in X

We can find an average slope between two points.

But how do we find the slope at a point?

There is nothing to measure!

But with derivatives we use a small difference ...

... then have it shrink towards zero.

Let us Find a Derivative!

We will use the slope formula:

Slope  =	Change in Y	=	Δy
	Change in X		Δx

We write dx instead of "Δx heads towards 0", so "the derivative of" is commonly written 

x² = 2x
"The derivative of x² equals 2x"
or simply "d dx of x² equals 2x"

so we can generalise as

What does x² = 2x mean?

It means that, for the function x², the slope or "rate of change" at any point is 2x.

So when x=2 the slope is 2x = 4, as shown here:

Finding differentiation by formula

 

Finding coordinates on the curve by using 

 differentiation:

Second order derivative

Finding equation of tangents and normals by using differentiation

TheTangent

The Normal

Example explained

Example

Solution-1

Solution for c

Solution for d

You can also look into 

https://www.youtube.com/watch?v=GMVqLsmlXnM