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): \( \dfrac{1}{ax^2+bx+c}\)

Let f(x) \( \dfrac{1}{ax^2+bx+c}\)

By quotient rule,

\(f'(x)=\dfrac{ax^2+bx+c\dfrac{d}{dx}(1)-\dfrac{d}{dx}(ax^2+bx+c)}{ax^2+bx+c}\)

\(\dfrac{(ax^2+bx+c)(0)-(2ax+b)}{(ax^2+bx+c)^2}\)

\( \dfrac{-(2ax+b)}{(ax^2+bx+c)^2}\)

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