Math Doubts

Derivative of cscx formula


$\dfrac{d}{dx}{\, (\csc{x})} \,=\, -\csc{x}\cot{x}$

The derivative or differentiation of cosecant function with respect to a variable is equal to the negative the product of cosecant and cotangent functions. This derivative rule is read as the derivative of $\csc{x}$ function with respect to $x$ is equal to the minus $\csc{x}$ times $\cot{x}$.


Take, $x$ as a variable, then according to trigonometry, the cosecant function is written as $\csc{x}$ or $\operatorname{cosec}{x}$ in mathematical form. The derivative of the cosecant function with respect to $x$ is written as the following mathematical form.

$\dfrac{d}{dx}{\, (\csc{x})} \,\,\,$ or $\,\,\, \dfrac{d}{dx}{\, (\operatorname{cosec}{x})}$

In differential calculus, the differentiation of the $\csc{x}$ function with respect to $x$ can be written as $\dfrac{d{\,(\csc{x})}}{dx}$ and also expressed as ${(\csc{x})}’$ simply.

Other form

The differentiation of the cosecant function formula can be written in the form of any variable.

$(1) \,\,\,$ $\dfrac{d}{dr}{\, (\csc{r})} \,=\, -\csc{r}\cot{r}$

$(2) \,\,\,$ $\dfrac{d}{dt}{\, (\csc{t})} \,=\, -\csc{t}\cot{t}$

$(3) \,\,\,$ $\dfrac{d}{dy}{\, (\csc{y})} \,=\, -\csc{y}\cot{y}$


Learn how to derive the derivative of the cosecant function from first principle in differential calculus.

Math Questions

The math problems with solutions to learn how to solve a problem.

Learn solutions

Math Worksheets

The math worksheets with answers for your practice with examples.

Practice now

Math Videos

The math videos tutorials with visual graphics to learn every concept.

Watch now

Subscribe us

Get the latest math updates from the Math Doubts by subscribing us.

Learn more

Math Doubts

A free math education service for students to learn every math concept easily, for teachers to teach mathematics understandably and for mathematicians to share their maths researching projects.

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved