Y=sinaXsinbX求Y的n阶导数

Question

Y=sinaXsinbX
求Y的n阶导数

Answer 1

Y = sinaxsinbx = 1/2[ cos(a-b)x - cos(a+b)x ]
y(n) = { 1/2[ cos(a-b)x - cos(a+b)x ] }(n)
= 1/2{ [cos(a-b)x](n) - [cos(a+b)x](n) }
= 1/2{ [ (a-b)^n*cos[(a-b)x + nπ/2] - (a+b)^n*cos[(a+b)x + nπ/2] }