What is the derivative of #5x arcsin(x)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Guilherme N. Jun 6, 2015 Using the product rule, which states that for a function #y=f(x)g(x)# its derivative will be #y'=f'(x)g(x)+f(x)g'(x)#, #(dy)/(dx)=5arcsinx+5x(1/(sqrt(1-x^2)))=5(arcsinx+x/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 1294 views around the world You can reuse this answer Creative Commons License