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# 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}

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