Question

Differentiate the following w.r.t.x:
${\sin }^{-1}\left(\cos 3x\right)$

Answer 1

$y={\sin }^{-1}\left(\cos 3x\right)$

Differentiating w.r.t. x,

$\frac{dy}{dx}=\frac{1}{\sqrt{1-{\cos }^{2}3x}}(-\sin 3x)\times 3$

$\frac{dy}{dx}=\frac{-3\sin 3x}{\sqrt{1-{\cos }^{2}3x}}$