Question

有方程确定的隐函数y=f(x)的导数1.y=1+xe^y 2.y=tan(x+y)

Answer 1

两边对x求导得
y=1+xe^y
y'=e^y+xe^y*y'
y'=e^y/(1-xe^y)
y=tan(x+y)
y'=sec^2(x+y)*(1+y')
y'=-sec^2(x+y)/tan^2(x+y)=-csc^2(x+y)