# Derivatives Rules of Hyperbolic functions

There are six derivative rules to evaluate the differentiation of the hyperbolic functions in differential calculus. So, learn every derivative formula of hyperbolic functions with mathematical proofs.

### Hyperbolic sine function

$\dfrac{d}{dx}{\,\sinh{x}} \,=\, \cosh{x}$

### Hyperbolic Cosine function

$\dfrac{d}{dx}{\,\cosh{x}} \,=\, \sinh{x}$

### Hyperbolic Tan function

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

### Hyperbolic Cot function

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

### Hyperbolic Secant function

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

### Hyperbolic Cosecant function

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

###### 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

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