Haven't done any derivatives in a long time, trying to work on a different subject involving calculus but can't remember this

I am embarrassed to even ask this...

The answer is telling me that the derivative with respect to t of 1/(1+it) is i/(1+it).

For some reason I feel that it should be -i/[(1+it)^2]. I don't know where my old calc book is. Can somebody refresh my memory?