Question

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed nonzero constants and m and n are integers):\(\frac{1}{ax^2+bx+c}\)

Answer 1

Let f(x)= \(\frac{1}{ax^2+bx+c}\)
By quotient rule,
f'(x)= (ax² + bx + c) \(\frac{d}{dx}\) (1) - \(\frac{d}{dx}\)\(\frac{ax^2+bx+c}{(ax^2+bx+c)^2}\)
=(ax²+ bx+c)(0)-\(\frac{2ax+b}{(ax^2+bx+c)^2}\)
=\(-\frac{(2ax+b)}{(ax^2+bx+c)^2}\)