The derivative of a polynomial function

To calculate the derivative of a polynomial function, first, you should know the product rule of derivatives and the basic rule of the derivative.

Product rule of derivative

(Here n can be either positive or negative value)

Understand in this way: The old power of the variable is multiplied with the coefficient of the variable and the new power of the variable is decreased by 1 from the old power. 

Example: Find the derivative of x³?

Solution:

Let y = x³

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Some basic rules of derivative

• If y = c f(x)

• If y = c

Example 1: Find the derivative of 4x³ + 7x?

Solution:

Let y = 4x³ + 7x

Example 2: Find the derivative of 3x² – 7?

Solution:

Let y = 3x² – 7

Derivatives are used in Calculus to measure the rate of change of a function with respect to a variable. The use of derivatives is very important in Mathematics. It is used to solve many problems in mathematics like to find out maxima or minima of a function, slope of a function, to tell whether a function is increasing or decreasing. If a function is written as y = f(x) and we want to find the derivative of this function then it will be written as dy/dx and can be pronounced as the rate of change of y with respect to x.