Partial Derivative

  1. I'm trying to figure out this equation.

    [tex]
    {\Psi} = Ae^{-a(bx-ct)^2}
    [/tex]

    I've expanded this to

    [tex]
    {\Psi} = Ae^{-ab^2x^2-abxct-ac^2t^2}
    [/tex]

    When I try to find the derivative I get this

    [tex]
    \left(\newcommand {\pd}[3]{ \frac{ \partial^{#3}{#1} }{ \partial {#2}^{#3} } }

    \pd{\Psi}{t}{}\right)_x = (-2ac^2t-abxc)Ae^{-ab^2x^2-abxct-ac^2t^2}
    [/tex]

    I should get this instead

    [tex]
    \left(\newcommand {\pd}[3]{ \frac{ \partial^{#3}{#1} }{ \partial {#2}^{#3} } }

    \pd{\Psi}{t}{}\right)_x = (-2abcx-2ac^2t)Ae^{-ab^2x^2-abxct-ac^2t^2}
    [/tex]

    Can anyone tell me where my error is and how I can fix it?
     
    Last edited: Oct 5, 2005
  2. jcsd
  3. krab

    krab 905
    Science Advisor

    Try again in expanding
    [tex](bx-ct)^2[/tex]
     
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