From Math Images
I get what you're saying about the general problem. I think we should specify that this is for scalar functions only at the beginning of the piece to avoid more major rewriting.
In terms of that sentences, I agree with you, but I'm struggling on rephrasing it. If you have ideas, jump on in.
Yes, your last point makes sense--I'll edit that now.
So here are the things I object to:
A partial derivative is the derivative of a several-variable function with respect to only one variable. This sentence makes it ambiguous as to whether the output or the input has several variables.
In general there's the problem that Brendan (I'm guessing that Brendan is the author) seems to restrict his definition of partial derivatives to scalar fields. If we want to limit the scope of the page that way, maybe we should state at the beginning of the article that that's what we are doing.
Anyway, I didn't change this stuff because I'd love your thoughts on how to deal with this issue.
Finally, does it make sense to you to replace "they do not contain a y-factor" with "their value does not depend on y" or "their value is constant as long as x and z are held constant" or something like that?