Partial differentiation of a function

  • Thread starter Topdeck
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  • #1
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Hi, I've got the following problem:

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

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 [tex]\frac{\partial{z}}{\partial{x}}[/tex]. I don't really know how to treat the [tex]f(u)[/tex]. Any pointers?

Thanks,
Toppers
 

Answers and Replies

  • #2
1,101
3
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).
 
  • #3
2
0
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
 

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