急用,Y=正切X+Y的二阶导数计算过程,

Question

急用,Y=正切X+Y的二阶导数计算过程,

Answer 1

y'=[sec(x+y)]^2(1+y')=y'[sec(x+y)]^2+[sec(x+y)]^2
∴y'{1-[sec(x+y)]^2}=[sec(x+y)]^2
y'=[sec(x+y)]^2/{1-[sec(x+y)]^2}
y''=={2[sec(x+y)][sec(x+y)]'(x+y)'{1-[sec(x+y)]^2}-[sec(x+y)]^2*(-2)[sec(x+y)[sec（x+y)]'(x+y)']}/{1-[sec(x+y)]^2}^2
={2(1+y')[sec(x+y)]^2[tan(x+y)]{{1-[sec(x+y)]^2}+2[sec(x+y)]^4[tan(x+y)](1+y')}/{1-[sec(x+y)^2}^2
进一步化简并将y'代入得y''