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): (px + q)(r/x + s)

Solution:

The given function is f(x) = (px + q)(r/x + s).

Using the product rule, its derivative is,

f'(x) = (px + q) d/dx (r/x + s) + (r/x + s) d/dx (px + q)

= (px + q) (-r/x² + 0) + (r/x + s) (p · 1 + 0) [using the derivative formula, d/dx (xⁿ) = n x^n-1]

=  -pr/x - qr/x² + pr/x + ps

= - qr/x² + ps

NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 3

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): (px + q)(r/x + s)

Summary:

The derivative of the given function (px + q)(r/x + s) is - qr/x² + ps