Question
Diffrentiate the following w.r.t.x
$\log \left[\cos \left(x^3-5\right)\right]$
$\log \left[\cos \left(x^3-5\right)\right]$
Differentiating w.r.t. x, we get
$\frac{d y}{d x}=\frac{d}{d x}\left\{\log \left[\cos \left(x^3-5\right)\right]\right\}$
$\begin{aligned} & =\frac{1}{\cos \left(x^3-5\right)} \cdot \frac{d}{d x}\left[\cos \left(x^3-5\right)\right] \\ & =\frac{1}{\cos \left(x^3-5\right)} \cdot\left[-\sin \left(x^3-5\right)\right] \cdot \frac{d}{d x}\left(x^3-5\right) \\ & =-\tan \left(x^3-5\right) \times\left(3 x^2-0\right) \\ & =-3 x^2 \tan \left(x^3-5\right) .\end{aligned}$
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