How do you find the derivative of #arcsin(x/3)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Monzur R. Feb 22, 2017 See below Explanation: Let #y=arcsin(x/3)# #siny=x/3# #cosydy/dx=1/3# #dy/dx=1/(3cosy)=1/(3sqrt(1-(x/3)^2))# The general rule is for #f:x|->b arcsinx#, #f'(x)=1/sqrt(1-x^2)b# 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 1655 views around the world You can reuse this answer Creative Commons License