Question

y=sinx的4次方＋cosx的4次方的n阶导是什么

Answer 1

y=(sinx)^4+(cosx)^4=[(sinx)^2+(cosx)^2]^2-2(sinx)^2(cosx)^2
=1-(1/2)(sin2x)^2=1-(1/4)(1-cos4x)=3/4+(1/4)cos4x,
n 阶导数:y^(n) = cos(4x+nπ/2)