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Homework Help: Derivatives and differentials

  1. Mar 28, 2008 #1
    [SOLVED] Derivatives and differentials

    1. The problem statement, all variables and given/known data
    Hmm, when I have


    [tex]\frac{dx^2}{dx}[/tex], does this equal zero or 2x?

    What confuses me is the way it is written.
     
  2. jcsd
  3. Mar 28, 2008 #2
    Uh ... what is the original problem? And did you copy that exactly?

    1st derivative = [tex]\frac{d}{dx}[/tex]

    2nd derivative = [tex]\frac{d^2}{dx^2}[/tex]

    I think you meant ... [tex]\frac{d}{dx}(x^2)=2x[/tex] (which says ... this is the derivative of x ...) <--- just an example!

    It's not like [tex]\frac{dy}{dx}[/tex] ... which states that you're taking the derivative of y with respects to x.
     
    Last edited: Mar 28, 2008
  4. Mar 28, 2008 #3
    The original problem is:

    Consider the 2D Laplace equation in polar cylindricals. Assume the solutions u(rho, Phi) = rho^n * Phi(phi), where n > 0.

    I have to find u(rho, Phi).

    What they do in the solution is to find the solution for Phi(phi) = A*cos(...) + B*sin(...), and then they set the total solution u(rho, Phi) = \sum [ A*cos(...) + B*sin(...) ] * rho^n.

    So I got confused. They do not find the solution for rho^n, but they just multiply it on? That doesn't make sense since we have to take the deivate of rho in Laplace's eq. in 2D?
     
  5. Mar 28, 2008 #4
    That's beyond me ... :p
     
  6. Mar 28, 2008 #5
    Ok, but thanks for taking the time to look at it.

    If anybody else has a suggestion, I am all ears.
     
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