$\dfrac{d}{dx}{\, \operatorname{csch}{x}}$ $\,=\,$ $-\operatorname{csch}{x}\coth{x}$

The hyperbolic cosecant function is written as $\operatorname{csch}{x}$ in mathematical form, when $x$ represents a variable. The derivative of the hyperbolic cosecant function with respect to $x$ is written in the following mathematical form in differential calculus.

$\dfrac{d}{dx}{\, \operatorname{csch}{x}}$

The differentiation rule of the hyperbolic cosecant function is written simply as $(\operatorname{csch}{x})’$ in calculus. The differentiation of the hyperbolic cosecant function is equal to the negative sign of product of hyperbolic cosecant and cotangent functions.

$\implies$ $\dfrac{d}{dx}{\, \operatorname{csch}{x}}$ $\,=\,$ $-\operatorname{csch}{x}\coth{x}$

The derivative of hyperbolic cosecant function can also be written in terms of any variable in mathematics.

$(1) \,\,\,$ $\dfrac{d}{du}{\, \operatorname{csch}{(u)}}$ $\,=\,$ $-\operatorname{csch}{(u)}\coth{(u)}$

$(2) \,\,\,$ $\dfrac{d}{dt}{\, \operatorname{csch}{(t)}}$ $\,=\,$ $-\operatorname{csch}{(t)}\coth{(t)}$

$(3) \,\,\,$ $\dfrac{d}{dz}{\, \operatorname{csch}{(z)}}$ $\,=\,$ $-\operatorname{csch}{(z)}\coth{(z)}$

Learn how to prove the differentiation of hyperbolic cosecant in differential calculus from the first principle of differentiation.

Latest Math Topics

Mar 21, 2023

Feb 25, 2023

Feb 17, 2023

Feb 10, 2023

Jan 15, 2023

Latest Math Problems

Mar 03, 2023

Mar 01, 2023

Feb 27, 2023

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 math problems in different methods with understandable steps and worksheets on every concept for your practice.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved