x的1/x次方的导数等于多少?
x的1/x次方的导数等于多少?
数学人气:496 ℃时间:2019-09-09 17:57:00
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用对数求导法:记 y = x^(1/x),取对数,得 lny = (1/x)lnx,两边关于 x 求导,得 (1/y)*y' = -x^(-2)lnx + (1/x)*(1/x)= x^(-2)(1 - lnx),故所求的导数是 (1/y)*y' = -x^(-2)lnx + (1/x)*(1/x)= y*[x^(...
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