隐函数求导方程式e的y次方+xy-e=0两边对x求导得d(e的y次方+xy-e)/dx=e的y次方dy/dx+y+xdy/dx这一步看不明白,

Question

隐函数求导
方程式e的y次方+xy-e=0两边对x求导得
d(e的y次方+xy-e)/dx=e的y次方dy/dx+y+xdy/dx这一步看不明白,

Answer 1

e^y+xy-e=0两边对x求导∵y是x的函数∴e^y对x求导由链式法则知d(e^y)/dx=[d(e^y)/dy]*(dy/dx)=(e^y)(dy/dx)而xy对x求导由乘法公式知d(xy)/dx=x(dy/dx)+y(dx/dx)=x(dy/dx)+ye是常数,对x求导为0∴d(e^y+xy-e)/dx=d(e^y)...