Given that $y={{\sin }^{-1}}(\ln x)$, find an expression of \(\frac{\mathrm{d}y}{\mathrm{d}x}

Question

Given that $y={{\sin }^{-1}}(\ln x)$, find an expression of $\frac{\mathrm{d}y}{\mathrm{d}x}$.

Accepted Answer

$\frac{1}{x\sqrt{1-{{(\ln x)}^{2}}}}$

Techniques of Differentiation - Derivatives of Natural Logarithmic Functions