Derivative Rules of Inverse trigonometric functions

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.

Inverse Sine function

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

Inverse Cosine function

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

Inverse Tangent function

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

Inverse Cotangent function

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

Inverse Secant function

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

Inverse Cosecant function

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