# Derivative of Hyperbolic Sine function

## Formula

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

### Introduction

Let $x$ denotes a variable, the hyperbolic sine function is written as $\sinh{x}$ in mathematical form. The derivative of the hyperbolic sin function with respect to $x$ is written as follows.

$\dfrac{d}{dx}{\, \sinh{(x)}}$

It can be simply written in mathematical form as $(\sinh{x})’$ in differential calculus.

The differentiation of the hyperbolic sin function is equal to the hyperbolic cosine function.

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

#### Other forms

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

#### Example

$(1) \,\,\,$ $\dfrac{d}{dk}{\, \sinh{k}}$ $\,=\,$ $\cosh{k}$

$(2) \,\,\,$ $\dfrac{d}{dm}{\, \sinh{m}}$ $\,=\,$ $\cosh{m}$

$(3) \,\,\,$ $\dfrac{d}{dz}{\, \sinh{z}}$ $\,=\,$ $\cosh{z}$

### Proof

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

Latest Math Topics
Apr 18, 2022
Apr 14, 2022

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 maths problems in different methods with understandable steps.

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.