Question

What's the derivative of `arctan(2x)`?

Answer 1

`2/(1+4x^2)`

Explanation:

using `d/dx (tan^-1x) = 1/(1+x^2)`

differentiating using the `color(blue)(" chain rule ")`

here x = 2x , hence

`rArr d/dx(tan^-1 2x) = 1/(1+(2x)^2) d/dx(2x)`

`= 1/(1+4x^2) .2 = 2/(1+4x^2)`