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If y = x/z then how do you calculate dx/dy?

  1. Aug 12, 2009 #1
    sorry im so dumb, coz i forgot all maths over the holidays..

    but if y = x/z
    then how do you calculate dx/dy?
     
  2. jcsd
  3. Aug 12, 2009 #2

    jgens

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    Gold Member

    Re: differentiation

    Well, if [itex]y = x/z[/itex] then [itex]z*y = x[/itex]. Does that help? If [itex]z[/itex] is a variable and not a constant, then you'll need to use partial derivatives.
     
  4. Aug 12, 2009 #3
    Re: differentiation

    haha i think that you underestimate how dumb i am. But that's cool, thanks for the help but
     
  5. Aug 12, 2009 #4

    jgens

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    Gold Member

    Re: differentiation

    Well, if [itex]z[/itex] is a constant, then this derivative is a simple application of the power rule:

    [tex]\frac{d}{dy}(zy) = z = \frac{dx}{dy}[/tex]

    If [itex]z[/itex] is not a constant but a function rather, then we use partial derivatives so that we have:

    [tex]\frac{\partial}{\partial y}(zy) = z = \frac{\partial x}{\partial y}[/tex]

    It's also easy to derive these results using the definition of a derivative . . .
     
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