求由方程x^2y=e^(x+y)所确定的隐函数导数dy\dx
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求由方程x²y=e^(x+y)所确定的隐函数dy/dx...............................................................................................解：F(x，y)=x²y-e^(x+y)=0则dy/dx=-(∂F/∂x)/(∂F/∂y)=-[2xy-e^(x+y)]/[x²e^(x+y)]......................................
=[e^(x+y)-2xy]/[x²-e^(x+y)]..........................................................................................................................【若题目是：求由方程x^(2y)=e^(x+y)所确定的隐函数导数dy/dx】........................................................解：F(x，y)=x^(2y)-e^(x+y)=0...................................................................................................................则dy/dx=-(∂F/∂x)/(∂F/∂y)=-[2yx^(2y-1)-e^(x+y)]/[2x^(2y)lnx-e^(x+y)].........................................................
=[e^(x+y)-2xy]/[x²-e^(x+y)]..........................................................................................................................【若题目是：求由方程x^(2y)=e^(x+y)所确定的隐函数导数dy/dx】........................................................解：F(x，y)=x^(2y)-e^(x+y)=0...................................................................................................................则dy/dx=-(∂F/∂x)/(∂F/∂y)=-[2yx^(2y-1)-e^(x+y)]/[2x^(2y)lnx-e^(x+y)].........................................................
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