Some more examples on derivative of polynomials

Example 1: Find the derivative of ?

Solution:

This can be written as 

y = x⁻⁷

Example 2: Find the derivative of 7x⁵ + x³ − x?

Solution:

Let y = 7x⁵ + x³ − x

Example 3: Find the derivative of (x + 5)² + 6x³ − 4?

Solution:

Let y = (x + 5)² + 6x³ − 4

Example 4: Find the derivative of 6x³ + (6x + 5)² − 8x?

Solution:

Let y = 6x³ + (6x + 5)² − 8x

Example 5: Find the derivative of ?

Solution:

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.