Question:
Write the derivative of sinx with respect to cosx
Solution:
Let $u=\sin x$ and $v=\cos x$
$\Rightarrow \frac{d u}{d x}=\cos x$ and $\frac{d v}{d x}=-\sin x$
$\therefore \frac{\frac{d u}{d x}}{\frac{d v}{d x}}=\frac{\cos x}{-\sin x}$
$\Rightarrow \frac{d u}{d v}=-\cot x$
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