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)-$\frac{2ax+b}{(ax^2+bx+c)^2}$
=$-\frac{(2ax+b)}{(ax^2+bx+c)^2}$