Question

x³+y³+3xy=1求y一阶导数,二阶导数

Answer 1

x³+y³+3xy=1 (1) 求y一阶导数,二阶导数

x²+y²y'+ y+xy'= 0 (2)

y'(y²+x) = -(x²+y) y'= -(x²+y)/(y²+x) (3)

2x+y"y²+y'2yy'+y'+y+xy"=0 (4)

y"(y²+x)=-(2x+2yy'²+y')

y" = -(2x+2yy'²+y')/(y²+x) (5)

将(3)式 y'代入 (5) 就得到 y" 的表达式.