Find the derivative of the following functions (it is to be understood that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are integers): (ax + b)ⁿ

Solution:

The given function is f(x) = (ax + b)ⁿ. It can be written as f(x) = (ax + b) (ax + b) (ax + b) ... (ax + b) (n times).

Using the product rule, its derivative is,

d/dx (f(x)) = [ (ax + b) (ax + b) ... (ax + b) (n-1) times d/dx (ax + b)
+ (ax + b) (ax + b) ... (ax + b) (n-1) times d/dx (ax + b)
+ ... + (ax + b) (ax + b) ... (ax + b) (n-1) times d/dx (ax + b) ] (n times)

= (ax + b) (ax + b) ... (ax + b) (n-1) times [ a + a + ... + a (n times)]

= (ax + b)^n-1 [na]

= na (ax + b)^n-1

NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 12

Find the derivative of the following functions (it is to be understood that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are integers): (ax + b)ⁿ

Summary:

The derivative of the given function (ax + b)ⁿ is na (ax + b)^n-1