Question

设函数 z=x^2ln(xy), 求 a/x, a/y, (a^2)/(ax)^2y？

Answer 1

方法如下，请作参考：

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Answer 2

z = x^2ln(xy)
∂z/∂x = 2xln(xy) + yx^2/(xy) = 2xln(xy) + x
∂z/∂y = x x^2/(xy) = x^2/y
∂²z/∂x² = 2ln(xy) + 2xy/(xy) + 1 = 2ln(xy) + 3
∂²z/∂x∂y = 2x/y
∂²z/∂y² = - x^2/y^2