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): 1/(ax² + bx + c)

Solution:

The given function is f(x) = 1/(ax² + bx + c).

Using the quotient rule, its derivative is,

d/dx (f(x)) = [ (ax² + bx + c) d/dx (1) - 1 d/dx (ax² + bx + c) ] / (ax² + bx + c)²

= [ (ax² + bx + c) (0) - 1 (2ax + b) ] / (ax² + bx + c)²

= -(2ax + b) / (ax² + bx + c)²

The value of the differential of the function f(x) is -(2ax + b) / (ax2 + bx + c)^2

NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 7

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): 1/(ax² + bx + c)

Summary:

The derivative of the given function 1/(ax² + bx + c) is -(2ax + b) / (ax² + bx + c)²