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Numerade Educator



Problem 19 Easy Difficulty

Prove that $ \frac {d}{dx}$ (cot $ x $) = $ - csc^2 x. $


$\frac{d}{d x}(\cot x)=\frac{d}{d x}\left(\frac{\cos x}{\sin x}\right)=\frac{(\sin x)(-\sin x)-(\cos x)(\cos x)}{\sin ^{2} x}=-\frac{\sin ^{2} x+\cos ^{2} x}{\sin ^{2} x}=-\frac{1}{\sin ^{2} x}=-\csc ^{2} x$

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Video Transcript

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