`F(theta) = arcsin(sqrt(sin(theta)))` Find the derivative of the function. Simplify where possible.

Expert Answers
gsarora17 eNotes educator| Certified Educator

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

`F(theta)=sin^-1(sqrt(sin(theta)))`

`F'(theta)=(1/sqrt(1-sintheta)) * d/(d theta)sqrt(sintheta)`

`F'(theta)=(1/sqrt(1-sintheta)) *(1/2)(sintheta)^(-1/2) costheta`

`F'(theta)=costheta/((2sqrt(sintheta)sqrt(1-sintheta)))`