Partial differentiation question

Hi,

I’m wondering how to do this question, I was hoping to do it by finding df/du and df/do and finding that df/dv is equal to zero to show f is only a function of u,

But I can’t seem to get that from my working, any ideas?

I haven't done this for years, but I think if you express Df/Dx in terms of Df/Du and Df/Dv, and similarly for Df/Dy, then you can get to a stage where you can argue that Df/Dv = 0 (after substituting in the equation you're given).

(D = "partial derivative"; can't be a**ed to Latex!)

Ah I see that works, thank you! I often find these sorts of questions tricky as I don’t know where I should start, how do you think of a way to go about it, would you say it is trial and error, or procedural?? Or just up to practice?