What is the derivative of #arctan(x^2+1)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Trevor Ryan. Feb 27, 2016 #(2x)/(1+(x^2+1)^2)# Explanation: From the rules, #d/dxtan^(-1)[u(x)]=1/(1+u^2)*(du)/dx# we get #d/dxtan^(-1)(x^2+1)=1/(1+(x^2+1)^2)*2x# 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 1145 views around the world You can reuse this answer Creative Commons License