Question

The derivative of ${\sin }^{2}x$ with respect to ${\cos }^{2}x$ is

• A. ${\tan }^{2}x$
• B. $\tan x$
• C. $-\tan x$
• D. None of these

Answer 1

The correct option is D None of these

Let $u={\sin }^{2}x;v={\cos }^{2}x$

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

$\frac{du}{dx}=2\sin x\cos x=\sin 2x$

$\frac{dv}{dx}=-2\cos x\sin x=-\sin 2x$

Now, $\frac{du}{dv}=\frac{du/dx}{dv/dx}$

$=\frac{\sin 2x}{-\sin 2x}=-1$