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

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

Dec 13, 2023

Jul 20, 2023

Jun 26, 2023

Latest Math Problems

Jan 30, 2024

Oct 15, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved