Mathematics

Problem

Consider the function

g(x)=x\,\arcsin x

. Find

g'\!\left(\tfrac{1}{2}\right)

and choose the correct exact value below. a)

\displaystyle \frac{\pi}{6}+\frac{\sqrt{3}}{6}

\displaystyle \frac{\pi}{6}+\frac{\sqrt{3}}{3}

\displaystyle \frac{2\sqrt{3}}{3}

\displaystyle \frac{\pi}{12}+\frac{\sqrt{3}}{3}