Question

设函数y=y(x)是由方程e^xy=2x+y^3所确定的隐函数,求y'(x)

Answer 1

方程两边对x求导,把y看成x的复合函数：
e^(xy)(xy)'=2+3y^2y'
e^(xy)(y+xy')=2+3y^2y'
y'[xe^(xy)-3y^2]=2-ye^(xy)
y'=[2-ye^(xy)]/[xe^(xy)-3y^2]