首先,利用两次积化和差公式:sinXsin2Xsin3X=-(1/2)(cos3X-cosX)sin3X=-1/4(sin6X)+1/2(sin4X)+1/2sin(2X)分别设u1,u2,u3为-1/4(sin6X),1/2(sin4X),1/2sin(2X)

　　则u1的n阶导数为-1/4(sin(6X+n(π/2))*6^(n).....这个是复合函数求导

　　同理u2的n阶导数为1/2(sin(4X+n(π/2))*4^(n)

　　u3的n阶导数为1/2(sin(2X+n(π/2))*2^(n)

　　最后y的n阶导数=u1的n阶导数+u2的n阶导数+u3的n阶导数=-1/4(sin(6X+n(π/2))*6^(n)+1/2(sin(4X+n(π/2))*4^(n)+1/2(sin(2X+n(π/2))*2^(n)