1、一阶导数计算：
∵y=(4x+2)sin7x+cos^6(8x+10)
∴dy/dx
=4sin7x+7(4x+2)cos7x+6cos^5(8x+10)*[-sin(8x+10)]*8
=4sin7x+7(4x+2)cos7x-48cos^5(8x+10)*sin(8x+10).
2、二阶导数计算：
dy/dx=4sin7x+7(4x+2)cos7x-48cos^5(8x+10)*sin(8x+10).
再次求导，即可计算出二阶导数，有：
d^2y/dx^2
=28cos7x+28cos7x-49(4x+2)sin7x+1920cos^4(8x+10)sin^2(8x+10)-384cos^5(8x+10)cos(8x+10)
=56cos7x-49(4x+2)sin7x+1920cos^4 (8x+10)[1-cos^2(8x+10)]-384cos^6(8x+10)
=56cos7x-49(4x+2)sin7x+1920cos^4 (8x+10)-1920cos^6(8x+10)]-384cos^6(8x+10)
=56cos7x-49(4x+2)sin7x+1920cos^4 (8x+10)-2304cos^6(8x+10).
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-61440cos^3(8x+10)sin(8x+10)+110592cos^5(8x+10)sin(8x+10)
=-588sin7x-343(4x+2)cos7x+512cos^3(8x+10)sin(8x+10)[216cos^2(8x+10)-120].
