# Maple wrong about partial derivative of exponential function?

When I input this function in Maple:

f := (x, y) -> exp(x+xy-2*y)


And take the derivative:

diff(f(x, y), x);


exp(x + xy - 2 y)


But I would have expected it to be:

(1+y)exp(x+xy-2y)


Does anyone have an explanation for this?

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there is a typo in your code in definition of the function $f$: you have xy instead of x*y, so Maple thinks (!) that xy is another variable rather than the product of two –  Ilya Nov 23 '11 at 13:19
I don't use maple, but does it matter that you write $xy$ and not $x*y$ –  draks ... Nov 23 '11 at 13:21
Ah, silly me! It does indeed work when this is fixed. –  ChrKroer Nov 23 '11 at 13:22
I think that could be an answer, @Ilya. :) –  Ｊ. Ｍ. Nov 23 '11 at 13:24
Even in Mathematica xy is a variable, not a product. You have to write x y for Mathematica to interpret it as an implicit product. –  GEdgar Nov 23 '11 at 13:55
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Maple understand each (non-predefined) expression of the form abcde as one variable. It also works for Mathematica where abcde means one variable while a b c d e is understood as a product of $5$ variables. Spaces does not work for Maple formulas typed in plain text, so you have to use * each time you want to multiply (works as well for Mathematica).
Maple does interpret x y as multiplication if it is entered as 2D Math input, which is one of the two input forms recognized by its Standard GUI. The implicit multiplication of x y is not recognized when entered in (1D, plaintext) Maple Notation. –  acer Nov 23 '11 at 17:21