What is the derivative of #(arcsin(3x))/x#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Tiago Hands Apr 23, 2015 You can solve this problem by using the quotient rule . #y=(arcsin(3x))/x=u/v# #u=arcsin(3x)# #sinu=3x# #cosu*(du)/(dx)=3# #(du)/(dx)=3/cosu=3/sqrt(1-9x^2)# #v=x#, #(dv)/(dx)=1# #(dy)/(dx)=(x*3/sqrt(1-9x^2)-arcsin(3x)*1)/x^2# #(dy)/(dx)=1/(x^2)*{(3x)/sqrt(1-9x^2)-arcsin(3x)}# 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 5961 views around the world You can reuse this answer Creative Commons License