Is Wolfram Alpha wrong with a simple derivative?

Question

Let $f=\frac{x^2w(y-z)t}{18l}$

then (imho):

$\frac{\partial{f(x,y,z)}}{\partial{w}}=\frac{x^2t(y-z)}{18l}$

However Wolfram Alpha produces a quite different result:

Wolfram alpha result http://www.wolframalpha.com/input/?i=d[%28x^2w%28y-z%29t%29%2F%2818l%29%2Cw]

So who's wrong this time - me or the computer? If the latter, then why?

Answer 1

I assume you meant taking the derivative with respect to $w$.

You are right, obviously, and Alpha is wrong. As for why... who knows? Submit a ticket with Wolfram. If you put in explicit multiplications, it works: http://www.wolframalpha.com/input/?i=d[%28x^2*w*%28y-z%29*t%29%2F%2818*l%29%2Cw]

Answer 2

If you do $$\mathrm{D}\left[\frac{x^{2}w(y-z)t}{18l},w\right]$$ instead you will get the expected answer. Perhaps it doesn't parse "${2}w$" the way we might expect.