What's the derivative of #arctan(x/3)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Michael Mar 20, 2016 #f'(x)=3/(x^2+9)# Explanation: #f(x)=arctan(x/3)# Apply the chain rule: #f'(x)=1/((x/3)^2+1)xx1/3# #f'(x)=1/(3(x^2/9+1)# This can be simplified to: #f'(x)=3/(x^2+9)# 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 15234 views around the world You can reuse this answer Creative Commons License