ktpr2

I have

f[x_] := ax+b/2x+d
f'[x]

and I get

-2(ax+b)/(d+2x)^2

instead of

ad-2b/(d+2x)^2

Assuming the above, my answer, is correct, why does mathemetica give me its answer? Is it interpreting one of the variables as some kind of weird constant?