y=(4+x^2)arctanx/2,求二阶导数，过程写详细，谢谢

Question

二阶导数

Answer 1

y' = 2x arctanx/2 + (4+x^2)[1/(1+(x/2)^2] (1/2) (product rule + chain rule)
= 2x arctanx/2 + 2 (simplification)
y'' = 2 arctanx/2 + 2x[1/(1+(x/2)^2](1/2)
= 2 arctanx/2 + 4x/(4+x^2)本回答被网友采纳

Answer 2

y'=2xarctan(x/2)+(4+x^2)/2(1+x^2/4)
=2xarctan(x/2)+2
y''=2arctan(x/2)+2x/2(1+x^2/4)
=2arctan(x/2)+4x/(4+x^2)

Answer 3