[Math] 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

Wolfram is interpreting "$w(y-z)$" as a function of $y-z$, which clearly contains only y and z as variables. Try enclosing "$w$" in parentheses: $D[\frac{(x^2(w)(y-z)t)}{(18l)},w].$ It should work.