`y = x sin^-1(x) + sqrt(1 - x^2)` Find the derivative of the function. Simplify where possible.

Expert Answers
gsarora17 eNotes educator| Certified Educator

`y=xsin^-1(x) +sqrt(1-x^2)`

`y'=xd/(dx) sin^-1(x) + sin^-1(x) d/(dx) x + d/(dx)sqrt(1-x^2)`

`y'=x(1/sqrt(1-x^2)) + sin^-1(x) + (1/2)(1-x^2)^(-1/2)(-2x)`

`y'=x/sqrt(1-x^2) + sin^-1(x) +(-x)/sqrt(1-x^2)`

`y'=sin^-1(x)`