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### The Derivative of Cosecant

##### Contents

{\begin{align} {d \over {dx}} \csc\theta &= {d \over {dx}} \left( {1 \over {\sin\theta}} \right) \cr &= \left( {{\sin\theta{d \over{dx}}1 - 1{d \over {dx}}\sin\theta} \over {\sin^2\theta}} \right) \tag{Quotient rule} \cr &= \left( - {{\cos\theta} \over {\sin^2\theta}} \right) \cr &= - \left( {1 \over {\sin\theta}} \right) \left( {{\cos\theta} \over {\sin\theta}} \right) \cr {d \over {dx}} \csc\theta &= - \csc\theta\cot\theta \end{align}}

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Category: Math Calculus Trigonometry

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### March 16, 2018

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