Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Looking for a proof that u(x) du(x)/dx = 0.5 d(u(x)^2)/dx

  1. Apr 25, 2017 #1
    Can anyone help with a proper proof for the following relation, please?

    Code (Text):
    [tex] u(x) \frac{\partial u(x)}{\partial x} = \frac{1}{2} \frac{\partial u(x)^2}{\partial x}  [/tex]
    From simple calculations I agree that it's true, but it's been annoying me for a while that I can't find a proper mathematical proof for it.

    See, for example (between equations 4 and 5): http://fluid.itcmp.pwr.wroc.pl/~znmp/dydaktyka/fundam_FM/Lecture9_10.pdf

    Thanks!
     
  2. jcsd
  3. Apr 25, 2017 #2

    Orodruin

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member
    2017 Award

    Did you ever encounter the product rule for derivatives? Or the chain rule? Both work.
     
  4. May 25, 2017 #3
    let u*du/dx=y <=> 2(u*du/dx)=2y <=> u*du/dx+u*du/dx=2y (use inverse product rule a'b+ab'= (ab)' )
    <=> d/dx[u2]=2y <=> y=1/2 d/dx[u2]
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted