Math Doubts

Derivative of Hyperbolic Cotangent function


$\dfrac{d}{dx}{\, \coth{x}} \,=\, -\operatorname{csch}^2{x}$


When a variable is denoted by $x$, the hyperbolic cotangent function is written as $\coth{(x)}$ in mathematics. The derivative of the hyperbolic function with respect to $x$ is written in the following mathematical form in differential calculus.

$\dfrac{d}{dx}{\, \coth{x}}$

The derivative of the hyperbolic cotangent function is equal to the negative square of hyperbolic co-secant function.

$\implies$ $\dfrac{d}{dx}{\, \coth{(x)}} \,=\, -\operatorname{csch}^2{(x)}$

Alternative forms

The derivative rule of hyperbolic cotangent function can also be written in terms of any variable.

$(1) \,\,\,$ $\dfrac{d}{dl}{\, \coth{(l)}} \,=\, -\operatorname{csch}^2{(l)}$

$(2) \,\,\,$ $\dfrac{d}{dp}{\, \coth{(p)}} \,=\, -\operatorname{csch}^2{(p)}$

$(3) \,\,\,$ $\dfrac{d}{dz}{\, \coth{(z)}} \,=\, -\operatorname{csch}^2{(z)}$


Learn how to prove the derivative formula of the hyperbolic cotangent function from the first principle of the differentiation.

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