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$= \left(\frac{\partial^2 u}{\partial x^2} \frac{\partial x}{\partial s} + \frac{\partial^2 u}{\partial y \partial x} \frac{\partial y}{\partial s}\right) \frac{\partial u}{\partial x}e^s \cos t \\$

$= \frac{\partial^2 u}{\partial x^2} \frac{\partial x}{\partial s} \frac{\partial u}{\partial x}e^s \cos t + \frac{\partial^2 u}{\partial y \partial x} \frac{\partial y}{\partial s} \frac{\partial u}{\partial x}e^s \cos t \\$

I am not sure how you can simplify the following expression. I am having trouble with partial derivatives.

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"simplify" in what sense? Do we know something about $u$? –  martini Nov 12 '12 at 12:19
Hint: Multivariable chain rule –  dimensio1n0 Jun 2 '13 at 11:17

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