Derivative or differential coefficient of a function
Let y = f (x) be a function of x. Let x change by a value âˆ† x and let the corresponding change in y be âˆ† y. Then 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 exists as, 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 .
Note: The derivative of y with respect to x is also denoted as yâ€² or y_{1}
Example: Let a function f (x) = 2x
Then
Some standard derivative
Sl. No. 
Function, f(x) 
Derivative, fâ€²(x) 
1. 

0 
2. 


3. 


4. 

e ^{x} 
5. 


6. 


7. 

1 
8. 


9. 

