数学分析提高随机推荐裴礼文教材习题多元函数微分学6.2 偏导数与全微分多元函数微分繁琐不看本题本题讨论已掌握查看解析收入错题#17168设 z=f(x,y)z = f\left( {x,y}\right)z=f(x,y) 是二次连续可微函数,又有关系式 u=x+ay,v=x−ay(au = x + {ay},v = x - {ay}(au=x+ay,v=x−ay(a 是不为零的常数). 证明: a2∂2z∂x2−∂2z∂y2=4a2∂2z∂u∂v{a}^{2}\frac{{\partial }^{2}z}{\partial {x}^{2}} - \frac{{\partial }^{2}z}{\partial {y}^{2}} = 4{a}^{2}\frac{{\partial }^{2}z}{\partial u\partial v}a2∂x2∂2z−∂y2∂2z=4a2∂u∂v∂2z ,