Question

Help me to derivate this!!
f(x)=arcsinx^2

Answer 1

Let \[y=\sin^{-1} (x^{2})\]\[\sin y =x^{2}\]Using implicit differentiation
\[\frac{ d }{ dx }\sin y=\frac{ d }{ dx }x^{2}\]\[\cos y \frac{ dy }{ dx }=2x\]\[\frac{ dy }{ dx }=\frac{ 2x }{ \cos y }\]since \[\sin y = x^{2}\] \[\cos y= \sqrt{1-x^{2}}\]
\[\frac{ dy }{ dx }=\frac{ 2x }{ \sqrt{1-x^{2}} }, -1<x<1\]