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

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