Question

The derivative of $sinx$ with respect to $cosx$ is

• A. $sinx$
• B. $-cosx$
• C. $tanx$
• D. $-cotx$

Answer 1

Answer: (D)

Let $u(x)=\sin x$
and $v(x)=\cos x\Rightarrow \frac{du}{dx}=\cos x$
and $\frac{dv}{dx}=-\sin x$
Then, $\frac{du}{dv}=\frac{du/dx}{dv/dx}\Rightarrow \frac{du}{dv}=\frac{\cos x}{-\sin x}$
$\Rightarrow$ $\frac{du}{dv}=-\cot x$