It's been a little too long since I've has to do this. Can someone please remind me, how do you get from:(adsbygoogle = window.adsbygoogle || []).push({});

∂u/∂t = C(∂u/∂g)

to

∂^2u/∂t^2 = (C^2)(∂^2u/∂t^2)

The notation here is a little clumsy, but I'm just taking the second PDE of each side. How does the C^2 get there? Seems like it ought to be C but I can't put my finger on a proof either way.

By the way, this comes up in a derivation of the wave equation:

∂^2u/∂x^2 = (1/c^2)(∂^2u/∂t^2)

starting from

u(x,t) = u(x ± ct)

I'm sure someone out there knows this. Thanks for your help.

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# Simple PDE Question

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