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?
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)
-> $\displaystyle \frac{1 }{ \frac{ { x}^{2 } }{2 } +2 } = \frac{2 }{ {x}^{ 2} + 4} $
so you got it right