Question

y=1/(x^2-3x+2)，求y的n阶导数

Answer 1

y={1/[(x-1)(x-2)]}=(x-2)^(-1)-(x-1)^(-1)
y的n阶导数=[(-1)(-2)(-3)....(-n) × (x-2)^(-n-1)] - [(-1)(-2)(-3)....(-n) × (x-1)^(-n-1)]
=[(-1)^n]×n!×[ (x-2)^(-n-1) - (x-1)^(-n-1)]
a^b 就是a的b次方
n!就是n的阶乘=1×2×3×4......×(n-1)×n

Answer 2

y=((x-2)^-1)-((x-1)^-1);
y'=-1*((x-2)^-2)-(-1)*((x-1)^-2);
y(n)=(-1)*n!^*((x-2)^-(n+1))-(-1)*n!*((x-1)^-(n+1));