# Derivative of Hyperbolic Cosine function

## Formula

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

### Introduction

Let $x$ represents a variable, the hyperbolic cosine function is written as $\cosh{x}$ in mathematical form. The derivative of the hyperbolic cosine function with respect to $x$ is written in the following mathematical form.

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

The differentiation of the hyperbolic cosine function can be written simply in mathematical form as $(\cosh{x})’$ in differential calculus.

The derivative of the hyperbolic cosine function is equal to the hyperbolic sine function.

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

#### Other forms

The derivative of hyperbolic cosine function can be written in terms of any variable in differential calculus.

#### Example

$(1) \,\,\,$ $\dfrac{d}{dg}{\, \cosh{(g)}}$ $\,=\,$ $\sinh{(g)}$

$(2) \,\,\,$ $\dfrac{d}{dv}{\, \cosh{(v)}}$ $\,=\,$ $\sinh{(v)}$

$(3) \,\,\,$ $\dfrac{d}{dy}{\, \cosh{(y)}}$ $\,=\,$ $\sinh{(y)}$

### Proof

Learn how to prove the derivative of hyperbolic cosine function by the first principle of differentiation in differential calculus.

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