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)/(px² + qx + r)

Solution:

The given function is f(x) = (ax + b)/(px² + qx + r). Using the quotient rule, its derivative is,

d/dx (f(x)) = [(px² + qx + r) d/dx (ax + b) - (ax + b) d/dx (px² + qx + r) ] / (px² + qx + r)²

= [ (px² + qx + r) (a + 0) - (ax + b) (2px + q + 0) ] / (px² + qx + r)²

= [apx² + aqx + ar - 2apx² - axq - 2pbx - bq ] / (px² + qx + r)²

= [ -apx² - 2bpx + ar - bq] / (px²​​​​​​​ + qx + r)²

NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 8

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)/(px² + qx + r)

Summary:

The derivative of the given function (ax + b)/(px2 + qx + r) is [ -apx² - 2bpx + ar - bq] / (px²​​​​​​​ + qx + r)²