Question

If $y=\sin \sqrt{1-x^2}$, then find $\frac{dy}{dx}$.

Answer 1

We have,

$y=\sin \sqrt{1-x^2}$

On differentiating w.r.t $x$, we get

$\frac{dy}{dx}=\cos \sqrt{1-x^2}(\frac{1}{2\sqrt{1-x^2}}\times (0-2x))$

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

Hence, this is the answer.