What is the derivative of #arcsin(e^x)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer James Apr 25, 2018 The answer #1/dxarcsin(e^x)=[e^x/(sqrt(1-(e^x)^2)]]# Explanation: show the steps below #arcsin(u)=1/(sqrt(1-u^2)# #(du)/dxarcsin(u)=[1/(sqrt(1-u^2)]]*du# #arcsin(e^x)=1/(sqrt(1-(e^x)^2)# #1/dxarcsin(e^x)=[e^x/(sqrt(1-(e^x)^2)]]# 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 1706 views around the world You can reuse this answer Creative Commons License