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Partial differentiation of a function

  1. Aug 29, 2009 #1
    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
     
  2. jcsd
  3. Aug 29, 2009 #2
    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).
     
  4. Aug 31, 2009 #3
    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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