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Derivative of $$$\csc{\left(x \right)}$$$

The calculator will find the derivative of $$$\csc{\left(x \right)}$$$, with steps shown.

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Find $$$\frac{d}{dx} \left(\csc{\left(x \right)}\right)$$$.

Solution

The derivative of the cosecant is $$$\frac{d}{dx} \left(\csc{\left(x \right)}\right) = - \cot{\left(x \right)} \csc{\left(x \right)}$$$:

$${\color{red}\left(\frac{d}{dx} \left(\csc{\left(x \right)}\right)\right)} = {\color{red}\left(- \cot{\left(x \right)} \csc{\left(x \right)}\right)}$$

Thus, $$$\frac{d}{dx} \left(\csc{\left(x \right)}\right) = - \cot{\left(x \right)} \csc{\left(x \right)}$$$.

Answer

$$$\frac{d}{dx} \left(\csc{\left(x \right)}\right) = - \cot{\left(x \right)} \csc{\left(x \right)}$$$A

Related Notes: Definition of Derivative , Derivatives of Elementary Functions , Table of Derivatives , Related Rates , Studying Derivative Graphically , Optimization Problems , Applications to Economics , Constant Multiple Rule , Sum and Difference Rules , Product Rule , Quotient Rule , Chain Rule , Derivative of Inverse Function