Math Doubts

Differentiation of Hyperbolic cosine

Formula

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

Introduction

The hyperbolic cosine function appears in differentiation. So, we have to know the derivative of hyperbolic cosine function in differential calculus.

The hyperbolic cosine is written as $\cosh{(x)}$ in mathematical form if $x$ is considered as a variable. The derivative or differentiation of $\cosh{x}$ with respect to $x$ is expressed as $\dfrac{d}{dx}{\, \cosh{x}}$ mathematically in calculus. It is actually equal to the $\sinh{x}$.

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

Other form

The variable can be denoted by symbol but the derivative of the hyperbolic cosine function must be expressed in terms of the respective variable. You must remember it while dealing the differential calculus.

Example

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

$(2) \,\,\,$ $\dfrac{d}{dp}{\, \cosh{(p)}}$ $\,=\,$ $\sinh{(p)}$

$(3) \,\,\,$ $\dfrac{d}{dt}{\, \cosh{(t)}}$ $\,=\,$ $\sinh{(t)}$

The above example understands you that the differentiation of hyperbolic cosine is equal to hyperbolic sine.

Proof

Learn how to derive the derivative of hyperbolic cosine formula in differential calculus.



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