syntax - Why can't D[] be used in place here?

Possible Duplicate:

General::ivar is not a valid variable when plotting - what actually causes this and how to avoid it?

Beginner question:

Why can't I use D[] like that?

Plot[{Sin[x], D[Sin[x], x]}, {x, -2 Pi, 2 Pi}]

If I assign the result of D[] to a variable and put that variable in the list it works.

Answer

Plot has attribute HoldAll which means in this case that D[Sin[x], x] isn't evaluated until after x is replaced with some number, so you end up with something like D[Sin[-6.28], -6.28] etc. which causes the errors since you can't take a derivative with respect to a number.

One way to get around this is to use Evaluate to evaluate the derivative before the numbers are plugged in, i.e. to do something like

Plot[Evaluate[{Sin[x], D[Sin[x], x]}], {x, -2 Pi, 2 Pi}]

Mathematica graphics

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