What's the derivative of #arctan(8^x)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer A. S. Adikesavan Apr 15, 2016 #(8^x ln 8)/(1+8^(2x))# Explanation: Let u = #8^x=e^(x ln 8) and y = arc tan 8^x#. #d/dx(y)=d/du(y)d/dx(u)#. #=1/(1+u^2)(ln 8 e^(x ln 8))# #= (8^x ln 8)/(1+8^(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 1691 views around the world You can reuse this answer Creative Commons License