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)

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



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