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Derivative of U(X(t),t) with respect to t

  1. Oct 10, 2004 #1
    What is the derivative of U(X(t),t)?

    Is it Ut(Xt(t),t)?
  2. jcsd
  3. Oct 11, 2004 #2


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    Science Advisor

    In general, the derivative of U(x,y) with respect to t is, by the chain rule,
    Ux(x,y)xt+ Uy(x,y)yt.

    Notice that the derivatives of x and y are multiplied by U(x,y), not arguments in it!

    In the case that y= t, that reduces to
    Ux(x,y)(xt)+ Ut.
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