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)

Solution:

The given function is f(x) = (ax + b)/(cx + d). Using the quotient rule, its derivative is,

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

= [ (cx + d) (a (1) + 0) - (ax + b) (c(1) + 0) ] / [ (cx + d)²]

= [ acx + ad - acx - bc ] / [ (cx + d)²]

= (ad - bc) / [ (cx + d)²]

NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 5

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)

Summary:

The derivative of the given function (ax + b)/(cx + d) is (ad - bc) / [ (cx + d)²]