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Limits and Derivatives — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsLimits and Derivatives1 Mark
Question
Compute derivative of $g(x)=\cot x$
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Answer

By definition, $g(x)=\cot x=\frac{\cos x}{\sin x}$
We use the quotient rule on this function wherever it is defined.
$\frac{d }{d x} g(x)=\frac{d}{d x}(\cot x)=\frac{d}{d x}\left(\frac{\cos x}{\sin x}\right)$
$=\frac{(\cos x)^{\prime}(\sin x)-(\cos x)(\sin x)^{\prime}}{(\sin x)^{2}}$
$=\frac{(-\sin x)(\sin x)-(\cos x)(\cos x)}{(\sin x)^{2}}$
$=-\frac{\sin ^{2} x+\cos ^{2} x}{\sin ^{2} x}=-cosec ^{2} x$

This is the required derivative.

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