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Homework Help: Chain Rules

  1. Jun 2, 2008 #1
    It's been a while since I've taken calculus. I was going through the derivation of the work-energy theorem and came across this: dv/dt = (dv/dx)(dx/dt) which is supposed to be a result of the chain rule. Anyone care to explain and please simplify it as much as possible.

    Thanks!
     
  2. jcsd
  3. Jun 2, 2008 #2

    nicksauce

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    The chain rule is

    f(g(x))' = f'(g(x))g'(x)

    Now replace f with v, g with x, x with t,the first ' with d/dt, the second ' with d/dx (since f is a function of g aka x), and the third ' with d/dt and voila you have
    dv/dt = (dv/dx)(dx/dt)
     
  4. Jun 2, 2008 #3

    tiny-tim

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    Hi nothing123! :smile:

    If v is a function of x only, and x is a function of t only, then if you increase t by a small amount ∆t, then x increases by a small amount ∆x = (dx/dt)∆t. (1)

    But v also increases, by a small amount ∆v = (dv/dx)∆x. (2)

    So, combining (1) and (2):
    ∆v = (dv/dx)∆x = (dv/dx)(dx/dt)∆t. :smile:
     
  5. Jun 2, 2008 #4
    Great, thanks for your help guys.
     
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