The inverse trigonometric functions are involved in differentiation in some cases. Hence, it is essential to learn the derivative formulas for evaluating the derivative of every inverse trigonometric function. Here, the list of derivatives of inverse trigonometric functions with proofs in differential calculus.
$\dfrac{d}{dx}{\,(\sin^{-1}{x})} \,=\, \dfrac{1}{\sqrt{1-x^2}}$
$\dfrac{d}{dx}{\,(\cos^{-1}{x})} \,=\, -\dfrac{1}{\sqrt{1 -x^2}}$
$\dfrac{d}{dx}{\,(\tan^{-1}{x})} \,=\, \dfrac{1}{1+x^2}$
$\dfrac{d}{dx}{\,(\cot^{-1}{x})} \,=\, -\dfrac{1}{1+x^2}$
$\dfrac{d}{dx}{\,(\sec^{-1}{x})} \,=\, \dfrac{1}{|x|\sqrt{x^2-1}}$
$\dfrac{d}{dx}{\,(\csc^{-1}{x})} \,=\, -\dfrac{1}{|x|\sqrt{x^2-1}}$
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