求导:xy=x-e^xy,求dy/dx

学习 时间:2026-04-03 11:28:37 阅读:2925
求导:xy=x-e^xy,求dy/dx

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阔达的冰棍

飘逸的指甲油

2026-04-03 11:28:37

答:xy=x-e^(xy)e^(xy)=x-xy=x(1-y)两边对x求导:(xy)' e^(xy)=1-y-xy'(y+xy')e^(xy)=1-y-xy'ye^(xy)+xy'e^(xy)+xy'=1-y[ 1+e^(xy) ] xy'=1-y-ye^(xy)y'=dy/dx= [ 1-y -ye^(xy) ] / [ x+xe^(xy) ]

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  • 含蓄的大碗
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    2026-04-03 11:28:37

    答:xy=x-e^(xy)e^(xy)=x-xy=x(1-y)两边对x求导:(xy)' e^(xy)=1-y-xy'(y+xy')e^(xy)=1-y-xy'ye^(xy)+xy'e^(xy)+xy'=1-y[ 1+e^(xy) ] xy'=1-y-ye^(xy)y'=dy/dx= [ 1-y -ye^(xy) ] / [ x+xe^(xy) ]

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