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Partial derivatives using definition

  1. Apr 8, 2008 #1
    1. The problem statement, all variables and given/known data
    We are given a table where showing the points x and y and values of a function f(x,y).
    The function itself is not given.
    I have to find the partial derivatives f'x, f'y, f''xx, f''yy and f''xy around the point (2,3).

    2. Relevant equations
    I have to use the definition :
    f'x(2,3) = lim (h-->0) [f(2+h,3) - f(2,3)] / h

    3. The attempt at a solution
    Ok. So I easily found f'x and f'y. (h is found by looking at the xs and ys, h for f'x = -1 and 2 for f'y).
    My problem is finding the f''. My teacher is the kind that shows one definition and gives one example. I don't know how to find the f''s.

    If someone could just point the way, I'd be grateful.
  2. jcsd
  3. Apr 8, 2008 #2
    The definition of the second partials is just the partial derivatives of the first partials. Why couldn't you just use the same method as before?
  4. Apr 8, 2008 #3
    Well I know. It's easy to find the partial derivatives when we have the function. That I can find.
    But as I said, we have just done one example with the "definition", so I quite don't see how.

    It's like d[df/dx]/dx
    When you derivate the function you just assume y as constant.
    But when it comes to lim f(a+h,b)-f(a,b)/h, I just don't know how to express it.

    f'x = 0 and f'y = 2
    f''xx(2,3) = f'x [f(2+h, 3) - f(2,3) /h]
    = f(2+2h, 3) - f(2,3)/h ?

    I don't know really.
    And then again, I'm quite stupid :D
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