Derivatives of Inverse Trigonometric functions (Using MF 27) Q1

Derivatives of Inverse Trigonometric functions (Using MF 27) Q1

Find the derivative of the following functions with respect to \(x\):

\(y = \sin^{-1}(\ln x)\)
\(y = \cos^{-1}(3x - 1)\)
\(y = \tan^{-1}(3^{x})\)

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Answer:(i) \(\frac1{x\sqrt{1-(\ln x)^2}}\) (ii) \(-\sqrt{\frac3{x(2-3x)}}\) (iii) \(\frac{3^x\ln3}{1+3^{2x}}\)

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