e^xcosx的n阶导数

Question

e^xcosx的n阶导数

Answer 1

哥们你华理的吧,我刚也在找这题,找了半天没找着,最后还是自己解出来的,你看看解得对不~
y'=e^xcosx-e^xsinx=-(√2)e^xsin(x-π/4)
y''=e^xcosx-e^xsinx-e^xsinx-e^xcosx=-2e^xsinx
y'''=-2(e^xsinx+e^xcosx)=-(√2)^3 e^xsin(x+π/4)
y''''=-(√2)^4 e^xsin(x+2π/4)
.
所以y^(n)=-(√2)^n e^xsin(x+(n-2)π/4)