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

\[\frac{d}{dx} \sin^{-1}{(x)}\]

Use Inverse Trigonometric Differentiation: the derivative of \(\sin^{-1}{(x)}\) is \(\frac{1}{\sqrt{1-{x}^{2}}}\).

\[\frac{1}{\sqrt{1-{x}^{2}}}\]

Done