Differentiability Pathology

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This is a model of the graph of a function f(x,y), where every directional derivative D_u f exists at the origin, but f isn't differentiable there. The tangent line indicator shows that all directional derivatives exist, yet it's evident that no tangent plane exists. The formula for f(x,y) is given below: f(x,y) = r * sin(3 * theta), which translates to (3 * x^2 * y - y^3) / (x^2 + y^2).