1. Limited time only! Sign up for a free 30min personal 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!

Derivative of a function of a function - please help.

  1. Oct 28, 2014 #1
    Hi at 1 Hour and 9 minutes this professor makes a derivation which i do not understand

    He is lecturing on newtonian mechanics and states that if

    dv/dt = a (acceleration)

    Then

    v*dv/dt = a*v

    And then he says that this is the same as

    d(v^2/2)/dt

    But I just can't undrestand how he did that last part? I know how to apply the chain rule to the derivative of a funnction of a function but i can't see how this applies in this example. The form he writes it on is f(x)*d(f(x)/dx (the same as v*dv/dt ) and the chain rule is on the form df(g(x))/dx = df(g)/dg * d(g(x))/dx? did he write it in a wrong mathematical form? What rule is he using?
     
  2. jcsd
  3. Oct 28, 2014 #2

    jedishrfu

    Staff: Mentor

    If you work it backward you get what he started with right?

    ie d( x^2) / dx = 2x and so 1/2 d( x^2 ) = x

    let u = v^2

    then du/dt = 2v dv/dt right?
     
  4. Oct 28, 2014 #3

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    All he says is ##{d\over dt} \left (v^2/2\right ) = v {dv\over dt}## right ?

    the rule he is using is that d/dg (g2/2) = g !


    if f = g2/2 and g = v your chain rule also says df/dg = g and df/dt = g dg/dt , in other words d/dt(v2 /2) = v dv/dt
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Derivative of a function of a function - please help.
Loading...