Compute the derivative of a given function

by RoRi

September 15, 2015

Compute the derivative of

$f(x) = \frac{ax^2 + bx + c}{\sin x + \cos x}.$

We compute,

$\begin{align*} f'(x) &= \frac{(2ax + b)(\sin x + \cos x) - (ax^2 + bx + c)(\cos x - \sin x)}{(\sin x + \cos x)^2} \\ &= \frac{(2ax+b)(\sin x + \cos x) + (ax^2 + bx + c)(\sin x - \cos x)}{1 + \sin (2x)}. \end{align*}$

Stumbling Robot

Compute the derivative of a given function

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