How do I find the derivative of F(x)=arcsin(sqrtsinx)?

1 Answer
Oct 27, 2015

F'(x)=cosx/(2sqrt(sinx)sqrt(1-sinx))

Explanation:

F(x)=f(g(x)) => F'(x)=f'(g(x))*g'(x)

F'(x)=1/sqrt(1-(sqrt(sinx))^2)*(sqrt(sinx))'

F'(x)=1/sqrt(1-(sqrt(sinx))^2) * 1/(2sqrt(sinx)) * (sinx)'

F'(x)=1/sqrt(1-sinx) * 1/(2sqrt(sinx)) * cosx

F'(x)=cosx/(2sqrt(sinx)sqrt(1-sinx))