The problem lies in g[x_] := D[f[x], x]; remember that what SetDelayed (that is, :=) does is to replace stuff on the right corresponding to patterns on the left before evaluating. Thus, when one does something like g[2] (and something like this happens within Plot[]), you are in fact evaluating D[f[2], 2], and since one cannot differentiate with respect to a constant ;), you get the General::ivar error message.

If you use Set instead (that is, g[x_] = D[f[x], x]), f[x] is differentiated first before the result of D[] is assigned to g[x_]. Since what's on the right of g[x_] is now an actual function, Plot[] no longer has a reason to complain.

The problem lies in g[x_] := D[f[x], x]; remember that what SetDelayed (that is, :=) does is to replace stuff on the right corresponding to patterns on the left before evaluating. Thus, when one does something like g[2] (and something like this happens within Plot[]), you are in fact evaluating D[f[2], 2], and since one cannot differentiate with respect to a constant ;), you get the General::ivar error message.

If you use Set instead (that is, g[x_] = D[f[x], x]), f[x] is differentiated first before the result of D[] is assigned to g[x_]. Since what's on the right of g[x_] is now an actual function, Plot[] no longer has a reason to complain.