How do you find the derivative of y=arcsine^x? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Trevor Ryan. Jan 18, 2016 dy/dx=e^x/sqrt(1-e^(2x) Explanation: From standard rules of differentiation we get dy/dx sin^(-1)(e^x)=1/sqrt(1-(e^x)^2)*e^x 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 1386 views around the world You can reuse this answer Creative Commons License