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Continuously differentiable

  1. Apr 26, 2009 #1
    1. The problem statement, all variables and given/known data

    Suppose that the function f: R^n --> R is continuously differentiable. Let x be a point in R^n. For p a nonzero point in R^n and alpha a nonzero real number, show that
    (df/d(alphap))(x)=alpha(df/d(p))(x)


    2. Relevant equations

    A function f: I --> R, defined on an open interval, is called continuously differentiable provided that it is differentiable and its derivative is continuous.

    3. The attempt at a solution

    Unfortunately, I do not have one. Which is why I am in dire need of help. I don't know where to begin. By the way, sorry for the horrible formatting, I am new to the forums.

    Edit: Okay, I might have an attempt at a solution.
    (df/d(alphap))(x)=<gradientf(x),alphap>=alpha<gradientf(x),p>=alpha(df/dp)(x)
     
    Last edited: Apr 26, 2009
  2. jcsd
  3. Apr 26, 2009 #2

    Dick

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    Homework Helper

    If df/d(p) means the directional derivative of f in the direction p, I think that looks ok.
     
  4. Apr 26, 2009 #3
    Oh, sorry. Yeah. I was talking about the directional derivative. I don't know how to write the actual notation for directional derivatives on here. And thank you for your help!
     
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