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Numerade Educator

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Problem 17 Easy Difficulty

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

Answer

$\frac{d}{d x}(\csc x)=\frac{d}{d x}\left(\frac{1}{\sin x}\right)=\frac{(\sin x)(0)-1(\cos x)}{\sin ^{2} x}=\frac{-\cos x}{\sin ^{2} x}=-\frac{1}{\sin x} \cdot \frac{\cos x}{\sin x}=-\csc x \cot x$

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Video Transcript

Hey, it's clear. So when you reign here, So our first steps gonna be taking the derivative of coast seeking, which is one over sign and we're gonna use the quotient role, Which gives us sign times zero minus one times co sign all over Sign square. This gives us negative co sign over a sign square, and this is negative. One over. Sign Times Co sign over a sign which gives us negative co secret tons co tangent.