Problem

Given that

$$y=3x\arcsin(2x)\qquad 0\le x\le \frac12$$

(a) determine an expression for $\dfrac{dy}{dx}$

(b) Hence determine the exact value of $\dfrac{dy}{dx}$ when $x=\frac14$, giving your answer in the form $a\pi+b$ where $a$ and $b$ are fully simplified constants to be found.