Question

已知dy/dx=2/2-cosy,求二阶导数d^2y/dx^2

Answer 1

dy/dx=2/(2-cosy)

即：

y'=2/(2-cosy)

y''

=-(2-cosy)'/(2-cosy)^2

=(cosy)'/(2-cosy)^2

=-siny*y'/(2-cosy)^2,将y'代入得到：

d^2y/dx^2 =y''=-2siny/(2-cosy)^3.