How do you differentiate #x^2arcsinx#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Alan P. Feb 19, 2015 Use the product rule for derivatives: # (d f(x) * g(x))/dx = (d f(x))/dx * g(x) + f(x) * (d g(x))/dx# with #f(x) = x^2# and #g(x) = arcsin x# (Note: #(d arcsin(x))/dx = 1/sqrt(1-x^2)# #(d (x^2 arcsin(x)))/dx = 2x * arcsin(x) + x^2 * 1/(sqrt(1 - 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 4096 views around the world You can reuse this answer Creative Commons License