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

  2. jcsd
  3. Apr 25, 2017 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    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]
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: Looking for a proof that u(x) du(x)/dx = 0.5 d(u(x)^2)/dx
  1. D/dx log(x^2+y^2) (Replies: 3)

  2. D/dx sinc(x) (Replies: 3)