Write the derivative of with respect to . - Vidyadip

Question

Write the derivative of $\sin\text{x}$ with respect to $\cos\text{x}$.

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Answer

Let $\text{u}=\sin\text{x}\text{ and v}=\cos\text{x}$
$\Rightarrow\frac{\text{du}}{\text{dx}}=\cos\text{x and }\frac{\text{dv}}{\text{dx}}=-\sin\text{x}$
$\therefore\frac{\frac{\text{du}}{\text{dx}}}{\frac{\text{dv}}{\text{dx}}}=\frac{\cos\text{x}}{-\sin\text{x}}$
$\Rightarrow\frac{\text{du}}{\text{dv}}=-\cot\text{x}$

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