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  1. adoion

    Scalar field 2 dimensional discontinuous but differentiable

    That's a great plot, thanks a lot. but I think I figured it out myself. the mistake I did was to assume that the vector tangent to the parabola would have one more point, besides the origin in common with the parabola. the expression depends on how one approaches the point ##(0,0)## and that's...
  2. adoion

    Scalar field 2 dimensional discontinuous but differentiable

    Hi, f(X)=\frac{xy^2}{x^2+y^4} is the function in question, this is the value of the function at ##X=(x,y)## when ##x\neq0##, and ##f(X)=0## when ##X=(0,y)## for any ##y## even ##y=0##. Now, along any vector or line from the origin the directional derivative ##f'(Y,0)## (where ##Y=(a,b)## is...
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