1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Homework Helper

    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

    User Avatar
    Science Advisor
    Homework Helper

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Chain Rules
  1. The chain rule (Replies: 7)

  2. Markov Chains (Replies: 7)

Loading...