What is the derivative of #ln(arctanx)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Trevor Ryan. Oct 18, 2015 #=1/((1+x^2)(tan^(-1)x))# Explanation: #d/dxln(tan^(-1)x)=1/(tan^(-1)x)*d/dxtan^(-1)x# #=1/(tan^(-1)x)*1/(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 7289 views around the world You can reuse this answer Creative Commons License