Question

Differentiate ${\sin }^{2}x$ with respect to $\tan x$.

Answer 1

Let $y={\sin }^{2}x$......(1) and $z=\tan x$.......(2).

Then we are to find $\frac{dy}{dz}$.

Now from (1) and (2) we get, $\frac{dy}{dx}=2\sin x\cos x$ and $\frac{dz}{dx}={\sec }^{2}x$.

So $\frac{dy}{dz}=\frac{\frac{dy}{dx}}{\frac{dz}{dx}}=\frac{2\sin x\cos x}{{\sec }^{2}x}=2\sin x.{\cos }^{3}x$