Vector calculus gradients

  1. 1. The problem statement, all variables and given/known data
    Find a function f(x,y,z) such that F = (gradient of F).

    3. The attempt at a solution
    I don't know :(
    I'm so confused
    Please help me!!
  2. jcsd
  3. tiny-tim

    tiny-tim 26,054
    Science Advisor
    Homework Helper

    hi calculusisrad! :smile:
    do you mean "Find a function f(x,y,z) such that F = (gradient of f)" ?

    (only scalars have gradients, there's no gradient of a vector)

    i don't understand either :confused:

    is either f or F given in the question?​
  4. Sorry, yes you're right. The gradient of f should not be bolded.
  5. Think about what a gradient is. If I told you to find the gradient of a function, what would you do?

    You would differentiate the function wrt x, and that is the i component of the gradient, you would differentiate the function wrt y, and that is the j component, and then you would differentiate the function wrt z, and that is the k component.

    Now, we are going in reverse. What is the reverse of differentiation?
  6. I completely forgot the biggest part of the problem. WOW. Sorry about that!!!

    Let F = (2xye^z)i + ((e^z)(x^2))j + ((x^2)y(e^z)+(z^2))k

    NOW find a function f(x,y,z) such that F = Gradient of f.

    Sorry about that. Please answer :)
  7. "Please answer"? How about you show some effort first? You should have read the forums rules by now.
  8. This was due last Thursday, I'm horribly behind on homework, I'm desperate here.
  9. Dick

    Dick 25,735
    Science Advisor
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    It's pretty easy to guess a form for f that works. Start guessing. That's often the easiest way to solve problems like this. What's a likely form for f given the first component of F?
    Last edited: Apr 4, 2012
  10. HallsofIvy

    HallsofIvy 40,310
    Staff Emeritus
    Science Advisor

    You know what the definition of "gradient" is, so use that.
    [itex]\frac{\partial f}{\partial x}=[/itex] what?
    [itex]\frac{\partial f}{\partial y}=[/itex] what?
    [itex]\frac{\partial f}{\partial z}=[/itex] what?
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