Question

The derivative of ${\cos }^{3}xw.r.t.{\sin }^3$ is

• A. $-\cot x$
• B. $\cot x$
• C. $\tan x$
• D. $-\tan x$

Answer 1

Answer: (A)

$-\cot x$

Let $u={\cos }^{3}x,v={\sin }^{3}x$
$\frac{du}{dx}=-3{\cos }^{2}x\sin x,\frac{dv}{dx}=3{\sin }^{2}x\cos x$
Now, $\frac{du}{dv}=\frac{-3{\cos }^{2}x\sin x}{3{\sin }^{2}x\cos x}$
$=-\frac{\cos x}{\sin x}$
$=-\cot x$