What's the answer to this problem? ?

there's a picture attached, and this is calculus

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  • Jeremy
    Lv 6
    1 month ago
    Favourite answer

    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

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