设函数y=f(x)由方程e^xy -2x^2-y=3所确定.求dy/dx

设函数y=f(x)由方程e^xy -2x^2-y=3所确定.求dy/dx
设函数y=f(x)由方程e^xy -2x^2-y=3所确定.求dy/dx

设函数y=f(x)由方程e^xy -2x^2-y=3所确定.求dy/dx
e^(xy)(y+xdy/dx)-4x-dy/dx=0；
dy/dx(xe^(xy)-1)=-ye^(xy)+4x；
dy/dx=(4x-ye^(xy))/(xe^(xy)-1).

答：
e^(xy)-2x^2-y=3
两边对x求导：
e^(xy)*(xy)'-4x-y'=0
e^(xy)*(y+xy')-4x-y'=0
[1-xe^(xy)]y'=ye^(xy)-4x
[1-x(2x^2+y+3)]y'=y(2x^2+y+3)-4x
dy/dx=(2yx^2+y^2+3y-4x) / (1-2x^3-xy-3x)