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I Chain rule in a multi-variable function

  1. May 7, 2016 #1
    Suppose you have a parameterized muli-varied function of the from ##F[x(t),y(t),\dot{x}(t),\dot{y}(t)]## and asked to find ##\frac{dF}{dt}##, is this the correct expression according to chain rule? I am confused because of the derivative terms involved.

    ##\frac{dF}{dt}=\frac{\partial F}{\partial x} \frac{dx}{dt} + \frac{\partial F}{\partial y} \frac{dy}{dt}##

    Or similar terms containing ##\dot{x}(t)## etc should also be included or it is something else altogether?
     
  2. jcsd
  3. May 7, 2016 #2

    Mark44

    Staff: Mentor

    If the function had parameters x, y, z, and w, the total derivative would have four terms, with the last two being ##\frac{\partial F}{\partial z} \frac{dz}{dt} + \frac{\partial F}{\partial w} \frac{dw}{dt}##. I believe that the derivative you're trying to find needs similar terms, with the partials being with respect to ##\dot{x}## and ##\dot{y}##.
     
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