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)(cx + d)²

Solution:

The given function is, f(x) = (ax + b)(cx + d)².

Using the product rule, its derivative is,

d/dx (f(x)) = (ax + b) d/dx (cx + d)² + (cx + d)² d/dx (ax + b)

= (ax + b) d/dx (c²x² + d² + 2cxd) + (cx + d)² (a(1) + 0)

= (ax + b) (2xc² + 0 + 2cd) + a (cx + d)² 

= 2c (ax + b) (cx + d) + a (cx + d)² 

NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 4

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)(cx + d)².

Summary:

The derivative of the given function (ax + b)(cx + d)² is 2c (ax + b) (cx + d) + a (cx + d)²