利用立方和公式sin^6x+cos^6x=(sin^2x+cos^2x)(sin^4x+cos^4x-sin^2xcos^2x)=sin^4x+cos^4x-sin^2xcos^2x=(sin^2x+cos^2x)^2-3sin^2xcos^2x=1-3sin^2xcos^2x=1-3/4·(sin4x)^2=5/8+3/8·cos8x所以,n阶导数为3/8·8^n...是的，被你的符号干扰了，呵呵利用立方和公式
sin^6x+cos^6x
=(sin^2x+cos^2x)(sin^4x+cos^4x-sin^2xcos^2x)
=sin^4x+cos^4x-sin^2xcos^2x
=(sin^2x+cos^2x)^2-3sin^2xcos^2x
=1-3sin^2xcos^2x
=1-3/4·(sin2x)^2
=5/8+3/8·cos4x
所以，n阶导数为
3/8·4^n·cos(4x+nπ/2)