What is the derivative of #arctan(8^x)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 1 Answer Bill K. Aug 26, 2015 #(ln(8)8^{x})/(1+8^{2x})# Explanation: Use the Chain Rule and the facts that #d/dx(arctan(x))=1/(1+x^2)# and #d/dx(8^{x})=ln(8) * 8^{x}# to get: #d/dx(arctan(8^{x}))=1/(1+(8^{x})^2) * d/dx(8^{x})# #=(ln(8)8^{x})/(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 1845 views around the world You can reuse this answer Creative Commons License