Question

Differentiate y=sqrt(1-x^2)sin^-1(x)

Answer 1

product rule for this one
\[(fg)'=f'g+g'f\] with
\[f(x)=\sqrt{1-x^2}, f'(x)=-\frac{x}{\sqrt{1-x^2}}, g(x)=\sin^{-1}(x), g'(x)=\frac{1}{\sqrt{1-x^2}}\]

Answer 2

I get xsin^-1x/(sqrt(1-x^2))+1 which is wrong. Where am I going wrong?