y=x^n/(1-x)
=(x^n-1)/(1-x)+1/(1-x)
=1/(1-x)-1-x-...-x^(n-1)
-1-x-...-x^(n-1) 的n阶导数=0
y的n阶导数=1/(1-x)的n阶导数:
[1/(1-x)]' = 1/(1-x)²
[1/(1-x)]'‘=-2/(1-x)³
.
y的n阶导数=1/(1-x)的n阶导数=(n!)【-1/(1-x)】^(n+1)
y=x^n/(1-x)
=(x^n-1)/(1-x)+1/(1-x)
=1/(1-x)-1-x-...-x^(n-1)
-1-x-...-x^(n-1) 的n阶导数=0
y的n阶导数=1/(1-x)的n阶导数:
[1/(1-x)]' = 1/(1-x)²
[1/(1-x)]'‘=-2/(1-x)³
.
y的n阶导数=1/(1-x)的n阶导数=(n!)【-1/(1-x)】^(n+1)