Why does Mathematica's D function give unexpected output for vector derivatives?

[Rasalhague]

Mathematica:

In[1]:= x = {(u + 2 v)/3, (u - v)/3, w}; D[x[u], u]

Out[1]= {1/3, 1/3, 0}[u] + {(u + 2 v)/3, (u - v)/3, w}’[u]

Why does it do this? Wolfram Alpha gives the answer I expected:

http://www.wolframalpha.com/input/?i=d%2Fdu+%28{%28u+%2B+2+v%29%2F3%2C+%28u+-+v%29%2F3%2C+w}%29

{1/3, 1/3, w’(u)} = {1/3, 1/3, 0} if w doesn't change with u.

 

[Simon_Tyler]

You defined
x = { ... }
without reference to u. So x was stored as { ... }.
Then you tried taking the derivative of x, which gets converted to
{ ... }
which doesn't make sense. If you ask for D[x,u] you will get what you wanted.

Wolfram Alpha has a more flexible grammar -- ie it's not a programming language.
Thus it guessed what you meant.

 

[Rasalhague]

Thanks, Simon. Problem solved. Yes, I've noticed before that WA is more forgiving and able to guess (for better or worse) at the meaning of ambigious syntax.