Math Doubts

Differentiation of inverse trigonometric functions

The inverse trigonometric functions are often involved in differential calculus. So, it is essential to learn the differentiation formulas to find the derivative of every inverse trigonometric function mathematically. The list of derivatives of inverse trigonometric functions are given here in terms of $x$.

Derivative of Arcsin(x)

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

Derivative of Arccos(x)

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

Derivative of Arctan(x)

$\large \dfrac{d}{dx}{\, \tan^{-1}{x}} \,=\, \dfrac{1}{1+x^2}$

Derivative of Arccot(x)

$\large \dfrac{d}{dx}{\, \cot^{-1}{x}} \,=\, \dfrac{-1}{1+x^2}$

Derivative of Arcsec(x)

$\large \dfrac{d}{dx}{\, \sec^{-1}{x}} \,=\, \dfrac{1}{|x| \sqrt{x^2 -1}}$

Derivative of Arccsc(x)

$\large \dfrac{d}{dx}{\, \csc^{-1}{x}} \,=\, \dfrac{-1}{|x| \sqrt{x^2 -1}}$

Math Doubts
Math Doubts is a best place to learn mathematics and from basics to advanced scientific level for students, teachers and researchers. Know more
Follow us on Social Media
Math Problems

Learn how to solve easy to difficult mathematics problems of all topics in various methods with step by step process and also maths questions for practising.

Learn more