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Homework Help: Calculus-differentiation Help Please

  1. Sep 25, 2005 #1
    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.

  2. jcsd
  3. Sep 25, 2005 #2
  4. Sep 25, 2005 #3
    Try using the chain rule to find [tex]\frac{\partial U}{\partial\theta} [/tex]. The do it agian to find the second derivatives. Hope it works!
  5. Sep 25, 2005 #4
    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
  6. Sep 25, 2005 #5
    No assumption. Just use [tex]\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}[/tex]
  7. Sep 25, 2005 #6
    its messy!
  8. Sep 25, 2005 #7
    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
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