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Total derivative and partial derivative

  1. Aug 18, 2014 #1
    can anyone tell me the difference of application of total derivative and partial derivative in physics?
    i still can't figure it out after searching on the internet
  2. jcsd
  3. Aug 18, 2014 #2


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    Gold Member

    A total derivative tells you how a quantity changes if another quantity changes, regardless on the kind of dependence of the first quantity on the second. But for a partial derivative, the second quantity should only appear explicitly in the expression giving the first quantity.
    For example consider [itex] y(x(t),t)=2x(t)^2+bt^2 [/itex], we'll have:
    \frac{\partial y}{\partial t}=2bt \\
    \frac{d y}{dt}=4x(t) \frac{dx(t)}{dt}+2bt
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