y=[x(x+1)/(x+2)e^x]^1/3怎么求其微分.y={x(x+1)/[(x+2)e^x]}^1/3

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y=[x(x+1)/(x+2)e^x]^1/3怎么求其微分.y={x(x+1)/[(x+2)e^x]}^1/3y=[x(x+1)/(x+2)e^x]^1/3怎么求其微分.y={x(x+1)/[(x+2

y=[x(x+1)/(x+2)e^x]^1/3怎么求其微分.y={x(x+1)/[(x+2)e^x]}^1/3
y=[x(x+1)/(x+2)e^x]^1/3怎么求其微分.
y={x(x+1)/[(x+2)e^x]}^1/3

y=[x(x+1)/(x+2)e^x]^1/3怎么求其微分.y={x(x+1)/[(x+2)e^x]}^1/3
等式两端取自然对数,有:
lny=(1/3)[lnx+ln(x+1)-ln(x+2)-x]
等式两端同时对x求导,有:
1/y*y导=(1/3)[1/x+1/(x+1)-1/(x+2)-1]
所以:y导=[x(x+1)/(x+2)e^x]^(1/3)*(1/3)[1/x+1/(x+1)-1/(x+2)-1]
所以:dy={[x(x+1)/(x+2)e^x]^(1/3)*(1/3)[1/x+1/(x+1)-1/(x+2)-1]}dx

不知道你这个e^x是放在分母那里还是分子那里的?