The expression you are plotting looks quite intricate and I did not try to understand it (I lose track of the order of operations). Normally I try to use notation that makes the order of operation obvious.
However, I was able to plot it and Manipulate it. I just changed {.1d,...} to {d,...}. The reason is this: you can prescribe the range where the variable d changes, but if you, instead, prescribe the interval where an expression that depends on d changes, then it may be too hard for Mathematica to figure out what you want. The expression you use (.1d) looks quite simple, but what if you wrote:
{Sin[Log[Tan[3*d^2-Sin[d]]]], -0.3,0.1}?
How would Mathematica decide what interval to use for d? I am not saying it is impossible, but in a sense you are asking Mathematica to solve a different problem, besides plotting. I also changed the range of k, because it looks like there is a pole at k=1. It is a bit tricky to plot poles in DiscretePlot. Plot usually produces something quite reasonable when the interval includes a simple pole.
Best,
OL.