# Thread: [SOLVED] Derivative of arctan[x/2]

1. ## [SOLVED] Derivative of arctan[x/2]

What is the derivative of arctan(x/2)??

I had a test today, so I eliminated some of the MC answers, and I guessed it was 2/x^2+4, but didn't show my work.. How do I do this?

2. Yeah so the derivative of arctan(x) is 1/(x^2+1)

If you have arctan(x/2) you can use the chain rule:

(d/dx) arctan(x/2) = [1/([x/2]^2+1)]*(1/2) = 1/([x^2]/2+1)

-> $\frac{1 }{ \frac{ { x}^{2 } }{2 } +2 } = \frac{2 }{ {x}^{ 2} + 4}$

so you got it right