# Inverse Trigonometric Differentiation

## Reference > Calculus: Differentiation

 Description$$\frac{d}{dx} \sin^{-1}{(x)}=\frac{1}{\sqrt{1-{x}^{2}}}$$ $$\frac{d}{dx} \cos^{-1}{(x)}=-\frac{1}{\sqrt{1-{x}^{2}}}$$ $$\frac{d}{dx} \tan^{-1}{(x)}=\frac{1}{1+{x}^{2}}$$ $$\frac{d}{dx} \csc^{-1}{(x)}=-\frac{1}{|x|\sqrt{1-{x}^{2}}}$$ $$\frac{d}{dx} \sec^{-1}{(x)}=\frac{1}{|x|\sqrt{1-{x}^{2}}}$$ $$\frac{d}{dx} \cot^{-1}{(x)}=-\frac{1}{1+{x}^{2}}$$
 Examples$\frac{d}{dx} \sin^{-1}{(x)}$1 Use Inverse Trigonometric Differentiation: the derivative of $$\sin^{-1}{(x)}$$ is $$\frac{1}{\sqrt{1-{x}^{2}}}$$.$\frac{1}{\sqrt{1-{x}^{2}}}$Done1/sqrt(1-x^2)