# 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 y1

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.