Question

求y={cos(x/2)}^2 的n阶导数

Answer 1

y= 0.5(1+cosx)

y'=-0.5(sinx)/2=0.5cos(x+π/2)

y"=-0.5(cosx)=0.5cos(x+π)

y"'=0.5(sinx)=0.5cos(x+3π/2)

y(4)=0.5(cosx)=0.5cos(x+2π)

.

y(n)=0.5cos(x+nπ/2)