西安毛子科技大学高阶导数XIDIANUNIVERSITY例5设 = f[xg(x)],其中f,g可导，求y,y"解y' = f(xg(x) (xg(x)= f'(xg(x) (2xg(x)+ xg(x)y" = (y')'=[f"(x’g(x) (2xg(x)+x’g'(x)] (2xg(x)+ x’g(x)+f'(xg(x) [2g(x)+2xg(x)+(2xg'(x)+ x2g"(x))高阶导数 例5 设 2 y f x g x = [ ( )]， 其中 f g, 可导, 求 y y   , . 2 2 y f x g x x g x    =  ( ( )) ( ( )) 2 2 =  + f x g x xg x x g x   ( ( )) (2 ( ) ( )) y y    = ( ) 2 2 2 =  +  + [ ( ( )) (2 ( ) ( ))] (2 ( ) ( )) f x g x xg x x g x xg x x g x    2 2 +  + + + f x g x g x xg x xg x x g x     ( ( )) [2 ( ) 2 ( )) (2 ( ) ( ))] 解