Can anyone help with a proper proof for the following relation, please?(adsbygoogle = window.adsbygoogle || []).push({});

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.Code (Text):[tex] u(x) \frac{\partial u(x)}{\partial x} = \frac{1}{2} \frac{\partial u(x)^2}{\partial x} [/tex]

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

Thanks!

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

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