What is the derivative of #tan^-1(4x)#? Calculus Differentiating Trigonometric Functions Differentiating Inverse Trigonometric Functions 2 Answers bp Apr 23, 2015 #4/(16x^2 +1)# Derivative of #tan^-1 4x# can be written using the formula for the derivative of #tan^-1x# = #1/(1+x^2)# #d/dx tan^-1 4x# = #1/(16x^2 +1) d/dx (4x)# = #4/(16x^2 +1)# Answer link Tiago Hands Apr 23, 2015 #y=arctan(4x)# #tany=4x# #sec^2y*(dy)/(dx)=4# #(tan^2y+1)*(dy)/(dx)=4# #(16x^2+1)*(dy)/(dx)=4# #(dy)/(dx)=4/(16x^2+1)# 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 20950 views around the world You can reuse this answer Creative Commons License