What is the derivative of tan^-1(4x)?

2 Answers
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)

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)