求y=(4x∧2-1)÷(x∧2-1)的n阶导数,

问题描述:

求y=(4x∧2-1)÷(x∧2-1)的n阶导数,

先化简
y=4+3/(x^2-1)=4+3/2[1/(x-1)+1/(x+1)]
下面就简单了:
y(n)=3/2(-1)^n*(n-1)![1/(x-1)^(n+1)+1/(x+1)^(n+1)]