Consider the function

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Consider the function g(x)=x arcsin⁡xg(x)=x\,\arcsin x. Find g′ ⁣(12)g'\!\left(\tfrac{1}{2}\right) and choose the correct exact value below. (a) π6+36\displaystyle \frac{\pi}{6}+\frac{\sqrt{3}}{6} (b) π6+33\displaystyle \frac{\pi}{6}+\frac{\sqrt{3}}{3} (c) 233\displaystyle \frac{2\sqrt{3}}{3} (d) π12+33\displaystyle \frac{\pi}{12}+\frac{\sqrt{3}}{3}

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