`y = cos^-1(sin^-1(t))` Find the derivative of the function. Simplify where possible.

Expert Answers
gsarora17 eNotes educator| Certified Educator

`d/(dx)cos^-1(x)=-1/sqrt(1-x^2)`

using above

`y=cos^-1(sin^-1(t))`

`y'=(-1)/sqrt(1-(sin^-1(t))^2) * d/(dt) sin^-1(t)`

`y'=(-1)/sqrt(1-(sin^-1(t))^2) * (1/sqrt(1-t^2))`

`y'=(-1)/(sqrt(1-t^2)sqrt(1-(sin^-1(t))^2))`