Question

how to differentiate sin (2. arcsin x)
ans: 2(1-2x^2)/ sqrt (1-x^2)

Answer 1

\[\sin (2\sin^{-1} )?\]

Answer 2

\[\sin (2\sin^{-1} x)\]

Answer 3

\[\Large\rm \sin(2 \arcsin x)\]Differentiate the outermost function first sin(stuff),\[\Large\rm \left[\sin(2\arcsin x)\right]'=\cos(2\arcsin x)\color{royalblue}{\left[2\arcsin x\right]'}\]And apply chain rule.
So we have to multiply by this blue part.
We need to take it's derivative.

Hmm your answer key looks nothing like this though.
Maybe they took a different approach.. thinking..