Answer
$\frac{dy}{dx}=\frac{-1}{(\cos^{-1}{x})(\sqrt{1-x^2})}$
Work Step by Step
$y=\ln{(\cos^{-1}{x})}$
On differentiating both sides:
$\frac{dy}{dx}=\frac{d(\ln{(\cos^{-1}{x}}))}{dx}$
$\frac{dy}{dx}=\frac{1}{\cos^{-1}{x}}\frac{d({(\cos^{-1}{x}}))}{dx}$
$\frac{dy}{dx}=\frac{-1}{(\cos^{-1}{x})(\sqrt{1-x^2})}$
