# D'alembert's solution to the wave equation, need help on Chain Rule

1. Jan 22, 2013

### kougou

1. The problem statement, all variables and given/known data

Please have a look at the picture attach, which shows the proof of the D'alembert's solution to the wave equation. If you can't open the open,
https://www.physicsforums.com/attachment.php?attachmentid=54937&stc=1&d=1358917223

The part I have problem is the taking the second paritial derivative of u with respect to x.
Ux=du/dz+du/dn, does this mean that Ux is a function of z and n, that is, Ux(z,n), and z(x,t) and n(x,t)?

so later when I taken the second derivative, then I apply chain rule?

Thank you

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2. Jan 23, 2013

### tiny-tim

hi kougou!

(try using the Quick Symbols box next to the Reply box )
i'm not really following your question

∂u/∂x can be considered either a function of x and y, or a function of ζ and η

since you want a final result in terms of ζ and η, you'll have to convert the derivatives wrt x and y into derivatives wrt ζ and η (and yes, you use the chain rule)