Find the gradient of f(x,y). f(x,y)=(x^2)e^-2y

  1. Here's the problem. Find the gradient of f(x,y). f(x,y)=(x^2)e^-2y.

    I don't have the solution to this and I need to know if I got the right gradient (I have more problems that depend on this gradient, points on it). I ended up getting, gradient f=<2xe^-2y, 2x-2e^-2y>. I don't think it's right, but can someone help me out here?
    Last edited by a moderator: Feb 6, 2013
  2. jcsd
  3. No.
    grad f= fx(x,y)i + fy(x,y)j
  4. HallsofIvy

    HallsofIvy 41,050
    Staff Emeritus
    Science Advisor

    Sorry, Stephen, you have fy wrong.

    The derivative of e-2y with respect to y is -2 e-2y The other factor, x2 is independent of y so treat it like a constant fy= (x2)(-2e-2y)= -2x2e-2y.

    The gradient of 2xe-2y is the vector <2x e-2y, -4xe-2y>.

    What ffrpg wrote: f=<2x^e-2y, 2x-2e^-2y> may be typos or just carelessness: x^e-2y doesn't make much sense and in "2x-2..." you MEANT (2x) times (-2), not 2x subtract 2...
  5. Ah yes. Where is my head?
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