1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Calculus-differentiation Help Please