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Derivative or differential coefficient of a function

Let y = f (x) be a function of x. Let x change by a value ∆ x and let the corresponding change in y be ∆ y. Then Description: 78707.png is known as the rate of change of y with respect to x. Differentiation measures this rate of change of one variable with respect to another.

If the limiting value of Description: 78721.png exists asDescription: 78727.png, it is called the derivative or the differential coefficient of y with respect to x. The derivative of y with respect to x is written as Description: 78733.png.

 

Description: 78739.png 

 

Description: 78746.png 

 

Note: The derivative of y with respect to x is also denoted as y′ or y1

 

Example: Let a function f (x) = 2x
Then Description: 78758.png 
Description: 78805.png 
Description: 78812.png

Some standard derivative

Sl. No.

Function, f(x)

Derivative, f(x)

1.

Description: 72638.png 

0

2.

Description: 78829.png 

Description: 72653.png 

3.

Description: 72660.png 

Description: 78881.png 

4.

Description: 72674.png 

e x

5.

Description: 72681.png 

Description: 78888.png 

6.

Description: 72695.png 

Description: 72702.png 

7.

Description: 72710.png 

1

8.

Description: 78864.png 

Description: 72726.png 

9.

Description: 78870.png 

Description: 72741.png 





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