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if [tex]x=\rho cos \phi[/tex] and [tex]y=\rho sin\phi[/tex]

prove that if U is a twice differentiable function of x and y that

[tex] \frac{d^2U}{dx^2} + \frac{d^2U}{dy^2} = \frac{d^2U}{d\rho^2} + \frac{1}{\rho}\frac{dU}{d\rho} + \frac{1}{\rho^2}\frac{d^2U}{d\phi^2}[/tex]

i am not sure how to approach this since the function is not given. Is there some assumption i am supposed to make about the function? like f(x,y) = xy or something?

any help on the first couple steps would be appreciated

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# Homework Help: Differentiation, change of variable

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