if $$x=\rho cos \theta$$ and $$y=\rho sin \theta$$

prove that if U is a twice differentiable function of x and y that
$$\frac{\partial^2U}{\partial x^2} + \frac{\partial^2 U}{\partial y^2} = \frac{\partial^2 U}{\partial \rho^2} + \frac{1}{\rho}\frac{\partial U}{\partial \rho} + \frac{1}{\rho^2}\frac{\partial^2 U}{\partial \theta^2}$$

I have absolutely no clue how to get started on this one.

thanks

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anyone...........

Try using the chain rule to find $$\frac{\partial U}{\partial\theta}$$. The do it agian to find the second derivatives. Hope it works!

I could try this except for the fact that i do not know what U equals...is there some assumption i am supposed to make here

No assumption. Just use $$\frac{\partial U}{\partial \theta } = \frac{\partial U}{\partial x} \frac{\partial x}{\partial \theta}+ \frac{\partial U}{\partial y} \frac{\partial y}{\partial \theta}$$

its messy!

i'm sorry i don't quite understand what i am supposed to be doing here. can i get a some explanation as to how and why to start this. i have really no idea here. thanks