Question

If $y=\cos \left[\log \left(\cot x\right)\right]$ then find $\frac{dy}{dx}$.

Answer 1

Given,

$y=\cos \left[\log \right(\cot x\left)\right]$.

Now, differentiating both sides with respect to $x$ we get,

$\frac{dy}{dx}=-\sin \left[\log \right(\cot x\left)\right].\frac{-cose{c}^{2}x}{\cot x}$

or, $\frac{dy}{dx}=\sin \left[\log \right(\cot x\left)\right].\frac{1}{\sin x.\cos x}$.