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Partial differentiation when the variable of integration is different

  1. Aug 3, 2011 #1
    Consider the partial differential of Q to the power of n w.r.t. x. How would you rearrange this expression so that it contains a partial derivative of Q w.r.t. x?
  2. jcsd
  3. Aug 3, 2011 #2


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    hi failexam! :smile:

    (have a curly d: ∂ :wink:)

    do you mean ∂Qn/∂x and ∂Q/∂x ?

    it's the same as with dQn/dx and dQ/dx
  4. Aug 3, 2011 #3


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    You talk about "partial derivative" but have only the single variable x.

    Assuming that Q is, in fact, a function of x, y, z, etc. then, by the chain rule,
    [tex]\frac{\partial Q^n}{\partial x}= n Q^{n-1}\frac{\partial Q}{\partial x}[/tex]
    which is, as tiny-tim said, the same as
    [tex]\frac{dQ^n}{dx}= n Q^{n-1}\frac{dQ}{dx}[/tex]
    ignoring the other variables.
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