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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 \(\frac{1}{\sqrt{1-{x}^{2}}}\). \[\frac{1}{\sqrt{1-{x}^{2}}}\] Done ![]() |
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