If $y=\cos^{-1}x$. Find $\frac{d^2y}{dx^2}$ in terms of y alone.

$-\csc^2y$ $\csc^2y\cot y$ $-\csc^2y\cot y$ $\csc^2y$

$-\csc^2y\cot y$

$\frac{dy}{dx}=\frac{-1}{\sqrt 1-x^2},$ putting $x=\cos y$ we get $\frac{dy}{dx}=-\csc y$. Differentiating w.r.to x again we get $\frac{d^2y}{dx^2}=-\frac{d}{dx}(\csc y)=-{-\csc y \cot y\frac{dy}{dx}}=-\csc^2y\cot y$