已知Z=(x+y)^(x-y),求Z'x,Z'y
求幂指数函数 Z=(x+y)^(x-y)的偏导数,万分感谢
用【对数求导法】先取对数lnZ=(x-y)ln(x+y),再求导: ①Zx/Z=ln(x+y)+(x-y)/(x+y) ===> Zx=[(x+y)^(x-y)][ln(x+y)+(x-y)/(x+y)] ②Zy/Z=-ln(x+y)+(x-y)/(x+y) ===> Zx=[(x+y)^(x-y)][-ln(x+y)+(x-y)/(x+y)] .
答:a^(m/n)=(n)^√(a^m) (a>0,m、n∈N*,且n>1) a^(-m/n)=1/[(n)^√(a^m)] (a>0,m、n∈N*,且n>1) l...详情>>
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