$\dfrac{d}{dx}{\, \cosh^{-1}{x}}$ $\,=\,$ $\dfrac{1}{\sqrt{x^2-1}}$

The inverse hyperbolic cosine function is expressed as $\cosh^{-1}{(x)}$ or $\operatorname{arccosh}{(x)}$ mathematically when the $x$ denotes a variable. The derivative of the inverse hyperbolic cosine function with respect to $x$ is expressed in the below mathematical forms.

$(1).\,\,\,$ $\dfrac{d}{dx}{\, (\cosh^{-1}{x})}$

$(2).\,\,\,$ $\dfrac{d}{dx}{\, (\operatorname{arccosh}{x})}$

In mathematics, the derivative of inverse hyperbolic cosine function is written as $(\cosh^{-1}{x})’$ or $(\operatorname{arccosh}{x})’$ simply in differential calculus.

The differentiation of hyperbolic inverse cos function with respect to $x$ is equal to reciprocal of the square root of difference of $1$ from $x$ squared.

$\implies$ $\dfrac{d}{dx}{\, \cosh^{-1}{x}}$ $\,=\,$ $\dfrac{1}{\sqrt{x^2-1}}$

The derivative of inverse hyperbolic cosine function can also be written in terms of any variable in mathematics.

$(1) \,\,\,$ $\dfrac{d}{de}{\, \cosh^{-1}{e}}$ $\,=\,$ $\dfrac{1}{\sqrt{e^2-1}}$

$(2) \,\,\,$ $\dfrac{d}{dm}{\, \cosh^{-1}{m}}$ $\,=\,$ $\dfrac{1}{\sqrt{m^2-1}}$

$(3) \,\,\,$ $\dfrac{d}{dz}{\, \cosh^{-1}{z}}$ $\,=\,$ $\dfrac{1}{\sqrt{z^2-1}}$

Learn how to prove differentiation rule of hyperbolic inverse cosine function by the first principle of differentiation.

Latest Math Topics

Dec 13, 2023

Jul 20, 2023

Jun 26, 2023

Latest Math Problems

Jan 30, 2024

Oct 15, 2023

Copyright © 2012 - 2023 Math Doubts, All Rights Reserved