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Math Help - whats the derivative of this function

  1. #1
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    whats the derivative of this function

     f(x) : R^{a} \longrightarrow R, f(x)=||x||, with || . || euclidean norm
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  2. #2
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    Quote Originally Posted by silversand View Post
     f(x) : R^{a} \longrightarrow R, f(x)=||x||, with || . || euclidean norm
    The derivative is the gradient.

    Notice that f(x_1,...,x_n) = \sqrt{x_1^2+....+x_n^2}.

    Therefore, \nabla f = \left( \frac{x_1}{\sqrt{x_1^2+...+x_n^2}}, ... , \frac{x_n}{\sqrt{x_1^2 + ... + x_n^2}} \right), so \nabla f(\bold{x}) = \frac{\bold{x}}{|\bold{x}|}.

    (This is just not differenciable at 0).
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