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Prove that gradients of functions f(x, y) = 1/2 log(x^2+y^2) and g(x, y) = arctan(x) are...

Prove that gradients of functions f(x, y) = 1/2 log(x^2+y^2) and g(x, y) = arctan(x) are orthogonal and have the same magnitude at any point different from origin.

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