?Assume that all the given functions are differentiable.If \(u=f(x, \ y)\), where
Chapter 12, Problem 50(choose chapter or problem)
Assume that all the given functions are differentiable.
If \(u=f(x, \ y)\), where \(x=e^{s} \cos \ t\) and \(y=e^{s} \sin \ t\), show that
\(\left(\frac{\partial u}{\partial x}\right)^{2}+\left(\frac{\partial u}{\partial y}\right)^{2}=e^{-2 s}\left[\left(\frac{\partial u}{\partial s}\right)^{2}+\left(\frac{\partial u}{\partial t}\right)^{2}\right]\)
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