- #1
thenewbosco
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calculus--differentiation Help Please!
if [tex]x=\rho cos \theta[/tex] and [tex] y=\rho sin \theta[/tex]
prove that if U is a twice differentiable function of x and y that
[tex]\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}[/tex]
I have absolutely no clue how to get started on this one.
thanks
if [tex]x=\rho cos \theta[/tex] and [tex] y=\rho sin \theta[/tex]
prove that if U is a twice differentiable function of x and y that
[tex]\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}[/tex]
I have absolutely no clue how to get started on this one.
thanks