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.

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