Math Doubts

Derivative of Hyperbolic Tangent function


$\dfrac{d}{dx}{\, \tanh{x}}$ $\,=\,$ $\operatorname{sech^2}{x}$


Let $x$ represents a variable, the hyperbolic tangent function is written as $\tanh{x}$ in mathematics. The derivative of the hyperbolic tan function with respect to $x$ is written as follows.

$\dfrac{d}{dx}{\, \tanh{(x)}}$ $\,=\,$ $\operatorname{sech^2}{(x)}$

It is simply written in mathematical form as $(\tanh{x})’$ in differential calculus.

The differentiation of the hyperbolic tan function is equal to the square of hyperbolic secant function.

$\implies$ $\dfrac{d}{dx}{\, \tanh{x}}$ $\,=\,$ $\operatorname{sech^2}{x}$

Other forms

The derivative of hyperbolic tangent can be written in terms of any variable in mathematics.


$(1) \,\,\,$ $\dfrac{d}{dp}{\, \tanh{(p)}}$ $\,=\,$ $\operatorname{sech^2}{(p)}$

$(2) \,\,\,$ $\dfrac{d}{dv}{\, \tanh{(v)}}$ $\,=\,$ $\operatorname{sech^2}{(v)}$

$(3) \,\,\,$ $\dfrac{d}{dy}{\, \tanh{(y)}}$ $\,=\,$ $\operatorname{sech^2}{(y)}$


Learn how to derive the differentiation of hyperbolic tangent in differential calculus by the first principle of differentiation.

Math Doubts

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

Maths Topics

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

Maths Problems

Learn how to solve the math problems in different methods with understandable steps and worksheets on every concept for your practice.

Learn solutions

Subscribe us

You can get the latest updates from us by following to our official page of Math Doubts in one of your favourite social media sites.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved