第1个回答 2016-06-08
f(x) = (x^2+1)cosx = (x^2+1)∑<n=0,∞>(-1)^n x^(2n)/(2n)!
= ∑<n=0,∞>(-1)^n [x^(2n+2)+x^(2n)]/(2n)!
n = 9 时 u<9> = (-1)^9 (x^20+x^18)/18!
x = 0 时,20阶导数值 f^(20)(0) = (-1)^9(20!/18!) = -380
n = 10 时 u<10> = (-1)^10 (x^22+x^20)/20!
x = 0 时,21阶导数值 f^(21)(0) = 0