# 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?

Original post by grhas98
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!)
Original post by davros
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?
Original post by grhas98
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?

This type of PDE change-of-variables question is relatively routine, I think.
It's just a matter of replacing all the f_x and f_y with f_u and f_v (by chain rule), then nice things happen, hopefully.
(Using exam-brain here, if nice things don't happen, you must have made errors somewhere)

Of course, this is routine only because we don't have to come up with the change of variables.