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

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.

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.

Latest Math Topics

Jul 24, 2022

Jul 15, 2022

Latest Math Problems

Sep 30, 2022

Jul 29, 2022

Jul 17, 2022

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved