Partial differentiation of a function

[Topdeck]

Hi, I've got the following problem:

Show that if $$z = x^nf(u)$$
and $$u = y/x$$
then $$x\frac{\partial{z}}{\partial{x}} + y\frac{\partial{z}}{\partial{y}} = nz$$

I know partial differentiation fairly well, but I've never seen one laid out like this before, and am not too sure how to get started (i.e. find $$\frac{\partial{z}}{\partial{x}}$$. I don't really know how to treat the $$f(u)$$. Any pointers?

Thanks,
Toppers

 

[snipez90]

Treat f(u) like a function to be differentiated using the chain rule. Just write f '(u) and then proceed to differentiating the inside (u) with respect to the x variable (for dz/dx).

 

[Topdeck]

Thanks snipez, just what I needed. Which was basically to just start writing down the equation and its answers one line after another. Normally with these "show that if x and y then z" questions I can't see the answer coming until the last line, and this was no different.

- Toppers