有两道高数隐函数求导，求帮忙。图画圈的这两道，。 {高数} 隐函数求导题两道
\u6c42\u4e24\u9053\u5927\u5b66\u9ad8\u6570\u9690\u51fd\u6570\u6c42\u5bfc\u9898\uff01\u5982\u56fe\u6240\u793a\uff1a
1.\u7528\u9690\u51fd\u6570\u5fae\u5206\u6cd5
\u4ee4F[x,y,z] = z³-3xyz-a³
z'x = -F'x/F'z = yz/(z²-xy)
z'y = -F'y/F'z = xz/(z²-xy)
(z\u4e5f\u662fy\u7684\u51fd\u6570\uff0c\u521a\u624d\u6211\u5f53\u6210\u5e38\u6570\u6254\u4e86- -!)
z''xy = [z'x]'y = [(yz)'(z² - xy) - yz * (2z z'y - x)]/(z²-xy)²
= [(z + y z'y)(z²-xy) - 2yz² z'y + xyz]/(z²-xy)²
= (z³ - yz² z'y - xy² z'y)/(z²-xy)²
= [z³ - (yz²+xy²)xz/(z²-xy)]/(z²-xy)²
= z(z^4 - 2xyz³ - x²y²z)/(z²-xy)³
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