2道同济六版课后隐函数求导题咋做啊，要详解，好的再加分！！！

Question

如题所述

Answer 1

(1)y=tan(x+y)
对x求导得y' = d(x+y)/dx * d(tan(x+y)) / d(x+y) = (1+y') * 1/cos^2(x+y)
所以cos^2(x+y) * y' = 1+y'化简得y'=-1/sin^2(x+y)
在对x求导得y'' = -(1+y') cos(x+y)/sin^3(x+y)
再将y'代入即得二阶导数
(2)xy=e^(x+y)
对x求导得y+xy'=(1+y')e^(x+y)
整理即得y‘