Math Doubts

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.

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