How do I find the derivative of F(x)=arcsin(sqrtsinx)? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Sasha P. 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)) Answer link Related questions What is the derivative of f(x)=sin^-1(x) ? What is the derivative of f(x)=cos^-1(x) ? What is the derivative of f(x)=tan^-1(x) ? What is the derivative of f(x)=sec^-1(x) ? What is the derivative of f(x)=csc^-1(x) ? What is the derivative of f(x)=cot^-1(x) ? What is the derivative of f(x)=(cos^-1(x))/x ? What is the derivative of f(x)=tan^-1(e^x) ? What is the derivative of f(x)=cos^-1(x^3) ? What is the derivative of f(x)=ln(sin^-1(x)) ? See all questions in Differentiating Inverse Trigonometric Functions Impact of this question 1635 views around the world You can reuse this answer Creative Commons License