What is the derivative of #(arctan x)^3#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Sharkbasket Mar 29, 2018 #d/dx(arctanx)^3=3((arctanx)^2)/(1+x^2)# Explanation: #f(x)=(arctanx)^3# We can find the derivative #f'(x)# using the chain rule. #f'(x)=3(arctanx)^2*color(red)(d/dxarctanx)# The derivative of #arctanx# can be found on most tables that list derivatives of trigonometric functions. #d/dxarctanx=1/(1+x^2)# #f'(x)=3(arctanx)^2*color(red)(1/(1+x^2))# #f'(x)=3((arctanx)^2)/(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 2049 views around the world You can reuse this answer Creative Commons License