Differentiate `x^cos^((-1)x)` with respect to `x` :

Explanation

\begin{equation}
\begin{aligned}
&\frac{d}{d x}\left(x \cos ^{-1} x\right) \\
&=\cos ^{-1} x \frac{d}{d x}(x)+x \frac{d}{d x}\left(\cos ^{-1} x\right) \\
&=1 \times \cos ^{-1} x+\left(-\frac{1}{\sqrt{1-x^{2}}}\right) x \\
&=\cos ^{-1} x-\frac{x}{\sqrt{1-x^{2}}}
\end{aligned}
\end{equation}