Question

Given f(x)=arctan(2x), find f’(x) in simplest form

Answer 1

Answer:

Step-by-step explanation:

$f(x)=tan^{-1} 2x\\let f(x)=y\\y=tan^{-1}2x\\tan y=2x\\diff. w.r.t.x\\sec^2y(\frac{dy}{dx} )=2\\\frac{dy}{dx} =\frac{2}{sec^2 y} =\frac{2}{1+tan^2y} =\frac{2}{1+(2x)^2} \\f'(x)=\frac{2}{1+4x^2}$