A question about PolyLog[n,x] function

Question

I know what PolyLog[0,-e^{-x}] means, but I do not know what does PolyLog^(1,0)[0,-e^{-x}] mean. Can someone tell me what does it mean?

Answer 1

It means derivative with respect to the first variable. Look up D and Derivative. Example with a general function f:

In[64]:= D[f[x, y], x]

Mathematica won't give any explicit symbolic form in the case of PolyLog, but it can compute (estimate??) numerical values.

Derivative[1, 0][PolyLog][2, 1] // N
(* -0.937548 *)