1、一阶导数计算：
∵y=(4x+2)sin7x+cos^6(9x+1)
∴dy/dx
=4sin7x+7(4x+2)cos7x+6cos^5(9x+1)*[-sin(9x+1)]*9
=4sin7x+7(4x+2)cos7x-54cos^5(9x+1)*sin(9x+1).
2、二阶导数计算：
dy/dx=4sin7x+7(4x+2)cos7x-54cos^5(9x+1)*sin(9x+1).
再次求导，即可计算出二阶导数，有：
d^2y/dx^2
=28cos7x+28cos7x-49(4x+2)sin7x+2430cos^4(9x+1)sin^2(9x+1)-486cos^5(9x+1)cos(9x+1)
=56cos7x-49(4x+2)sin7x+2430cos^4 (9x+1)[1-cos^2(9x+1)]-486cos^6(9x+1)
=56cos7x-49(4x+2)sin7x+2430cos^4 (9x+1)-2430cos^6(9x+1)]-486cos^6(9x+1)
=56cos7x-49(4x+2)sin7x+2430cos^4 (9x+1)-2916cos^6(9x+1).
3、三阶导数计算：
对二阶导数d^2y/dx^2再次对自变量x求导，则：
d^3y/dx^3
=-392sin7x-56sin7x-343(4x+2)cos7x-87480cos^3(9x+1)sin(9x+1)+157464cos^5(9x+1)sin(9x+1)
=-588sin7x-343(4x+2)cos7x+729cos^3(9x+1)sin(9x+1)[216cos^2(9x+1)-120].
