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): (px² + qx + r)/(ax + b)

Solution:

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

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

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

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

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

NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 9

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): (px² + qx + r)/(ax + b)

Summary:

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