Question

Differentiate w.r.t. x:

$y=cose{c}^{-1}\left(\frac{1}{\sqrt{1-x^2}}\right)$

Answer 1

Now,

$\begin{array}{c}y=\cos e{c}^{-1}\left(\frac{1}{\sqrt{1-x^2}}\right)\\ ={\sin }^{-1}\left(\sqrt{1-x^2}\right)\\ putx=\cos \theta \\ y={\sin }^{-1}\left(\sin \theta \right)\\ y=\theta \\ y={\cos }^{-1}x\\ \frac{dy}{dx}=-\frac{1}{\sqrt{1-x^2}}\end{array}$