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Math Help - Frechet Derivative

  1. #1
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    Frechet Derivative

    I'm trying to prove that f(r,s)=(r*cos(s),r*sin(s)) is differentiable using the definition of the Frechet derivative, that is:

    \lim_{h \to 0} \frac{ \| f(x + h) - f(x) - L*h   \|}{ \|h\|} = 0

    I know how to calculate the Frechet derivative, but I'm not sure how to "show that it's differentiable" using the above definition.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Write:

    Lh=\begin{pmatrix}{\cos s_0}&{-r_0\sin s_0}\\{\sin s_0}&{\;\;\;r_0\cos s_0}\end{pmatrix}\left({\begin{array}{ccc}{h_1}\\{  h_2}\end{array}\right)

    an compute the respective norms.

    Regards.

    Fernando Revilla
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