How do I find the derivative of #y=arcsin(e^x)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer mason m Nov 22, 2015 #(e^x)/(sqrt(1-e^(2x))# Explanation: Know that #d/dx[arcsin(u)]=(u')/(sqrt(1-u^2)#. #y'=(d/dx[e^x])/(sqrt(1-(e^x)^2))=(e^x)/(sqrt(1-e^(2x))# If you didn't already know that #d/dx[arcsin(u)]=(u')/(sqrt(1-u^2)# or want to know how to derive it, just tell me and I'll be happy to elaborate. 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 1926 views around the world You can reuse this answer Creative Commons License