求y=tan(x-y)的二阶导数是什么

Question

求y=tan(x-y)的二阶导数是什么

Answer 1

y=tan(x-y)两边求导y' = (1-y')/cos²(x-y)y' = 1/[1+cos²(x-y)]再次求导y" = -2cos(x-y)[-sin(x-y)](1-y')/[1+cos²(x-y)]²= sin(2x-2y)(1-y')/[1+cos²(x-y)]²= sin(2x-2y){1 - 1/[1+cos²(x-y)]}/[1+cos²(x-y)]²= sin(2x-2y)cos²(x-y)/[1+cos²(x-y)]³