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Chain rule.

  1. Nov 11, 2011 #1
    If a function is given by u = u(T,v) how to use the chain rule to write how u changes with respect to T & v.
    Please specify the steps involved.
    i understand chain rule as [itex]\frac{du}{dx}[/itex] = [itex]\frac{du}{dy}[/itex] [itex]\frac{dy}{dx}[/itex]
     
  2. jcsd
  3. Nov 11, 2011 #2

    mathman

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    Assuming T and v are both functions of x, the chain rule gives:
    du/dx = (∂u/∂T)(dT/dx) + (∂u/∂v)(dv/dx)
     
  4. Nov 11, 2011 #3
    very much thanks for ur quick response :)

    how does the symbol differs in meaning with d
     
  5. Nov 12, 2011 #4
    [itex] \partial [/itex] (read "partial") is basically the equivalent of [itex] d [/itex] in multivariable calculus, it means you take the derivative of a function with respect to a variable while considering all other variables as constants during that operation.

    For example if I have
    [tex] F = x^2 + 2xy + \frac{x}{y} [/tex]
    Then
    [tex] \frac{\partial F}{\partial x} = 2x + 2y + \frac{1}{y} [/tex]
    Can you find [itex] \frac{\partial F}{\partial y} [/itex]? :)
     
  6. Nov 12, 2011 #5
    = 2x - x/y2

    i think thats the right answer :)
     
  7. Nov 12, 2011 #6
    I think so too :)
     
  8. Nov 12, 2011 #7
    Appreciate ur help :)
     
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