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

The inverse hyperbolic sine function is written as $\sinh^{-1}{(x)}$ or $\operatorname{arcsinh}{(x)}$ in mathematics when the $x$ represents a variable. The derivative of the inverse hyperbolic sine function with respect to $x$ is written in the following mathematical forms.

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

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

Mathematically, the derivative of the inverse hyperbolic sine function is simply written as $(\sinh^{-1}{x})’$ or $(\operatorname{arcsinh}{x})’$ in differential calculus.

The differentiation of the hyperbolic inverse sin function with respect to $x$ is equal to multiplicative inverse of square root of sum of $1$ and $x$ squared.

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

In mathematics, the derivative of inverse hyperbolic sine function can also be written in terms of any variable.

$(1) \,\,\,$ $\dfrac{d}{db}{\, \sinh^{-1}{b}}$ $\,=\,$ $\dfrac{1}{\sqrt{b^2+1}}$

$(2) \,\,\,$ $\dfrac{d}{dl}{\, \sinh^{-1}{l}}$ $\,=\,$ $\dfrac{1}{\sqrt{l^2+1}}$

$(3) \,\,\,$ $\dfrac{d}{dy}{\, \sinh^{-1}{y}}$ $\,=\,$ $\dfrac{1}{\sqrt{y^2+1}}$

Learn how to prove the differentiation formula of hyperbolic inverse sine function by the first principle of differentiation.

Latest Math Topics

Jun 05, 2023

May 21, 2023

May 16, 2023

May 10, 2023

May 03, 2023

Latest Math Problems

May 09, 2023

A best free mathematics education website that helps students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

A math help place with list of solved problems with answers and worksheets on every concept for your practice.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved