What's the answer to this problem? ?

Question

there's a picture attached, and this is calculus

Answer 1

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f(x, y) = 5 * ln(x^2 + y^2)

f_x = [5/(x^2 + y^2)] * 2x = (10x)/(x^2 + y^2)

f_xy = (-10x * 2y)/(x^2 + y^2)^2 = (-20xy)/(x^2 + y^2)^2

f_y = [5/(x^2 + y^2)] * 2y = (10y)/(x^2 + y^2)

f_yx = (-10y * 2x)/(x^2 + y^2)^2 = (-20xy)/(x^2 + y^2)^2

Hence: f_xy = f_yx