x+1的0阶导数=x+1
x+1的1阶导数=1
2阶以上=0
sin2x的n阶导数=2的n次方sin(2x+nπ/2)
sin2x的n-1阶导数=2的n-1次方sin(2x+[n-1]π/2)
所以
y的n阶导数
=C(n,0)(x+1)2的n次方sin(2x+nπ/2)+C(n,1)2的n-1次方sin(2x+[n-1]π/2)
=(x+1)2的n次方sin(2x+nπ/2)+n·2的n-1次方sin(2x+[n-1]π/2)
x+1的0阶导数=x+1
x+1的1阶导数=1
2阶以上=0
sin2x的n阶导数=2的n次方sin(2x+nπ/2)
sin2x的n-1阶导数=2的n-1次方sin(2x+[n-1]π/2)
所以
y的n阶导数
=C(n,0)(x+1)2的n次方sin(2x+nπ/2)+C(n,1)2的n-1次方sin(2x+[n-1]π/2)
=(x+1)2的n次方sin(2x+nπ/2)+n·2的n-1次方sin(2x+[n-1]π/2)