Question

The derivative of $sin\, x$ with respect to $cos\text{ }x$ is

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

Answer 1

Answer: (D)

$-cot\,x$

Answer 2

Let $u(x)=\sin \,x$
and $v(x)=\cos \,x\,\,\,\Rightarrow \,\,\frac{du}{dx}=\cos \,x$

and $\frac{dv}{dx}=-\sin x$
Then, $\frac{du}{dv}=\frac{du/dx}{dv/dx}\Rightarrow \frac{du}{dv}=\frac{\cos \,x}{-\sin x}$
$\Rightarrow$ $\frac{du}{dv}=-\cot \,x$