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)