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What is this question referring to?

  1. Feb 20, 2013 #1
    1. The problem statement, all variables and given/known data
    What is this question en example of:
    Given u=lnsin(xy) show that


    2. Relevant equations
    du=cot(xy)(ydx + xdy)


    3. The attempt at a solution
    I think it is total differentiation.
     
  2. jcsd
  3. Feb 20, 2013 #2

    Simon Bridge

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    I'd call it implicit differentiation: ie.
    if ##u=xy##, then differentiating everything wrt x tells me $$\frac{du}{dx}=y+x\frac{dy}{dx} \Rightarrow du = ydx+xdy$$
     
  4. Feb 20, 2013 #3

    CompuChip

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    This is a convenient shortcut, but remember that [itex]\frac{du}{dx}[/itex] is not really a fraction, although it looks like one.

    Officially the definition is
    [tex]du = \frac{\partial u}{\partial x} \, dx + \frac{\partial u}{\partial y} \, dy[/tex]
    for u = u(x, y).
    That result du = y dx + x dy in Simon's example comes out correctly by "multiplying through by dx" is not completely co-incidental, but you should realise there's no real multiplication involved as "dx" is not really a number.
     
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