Differentiate the Series For $- \frac { 1 } { x }$

Multiple Choice

Differentiate the series for $- \frac { 1 } { x }$ to find the power series for the function $f ( x ) = \frac { 6 } { x ^ { 2 } }$ .

A) $6 \sum _ { n = 0 } ^ { \infty } ( - 1 ) ^ { n + 1 } n ( x - 1 ) ^ { n - 1 }$
B) $\sum _ { n = 1 } ^ { \infty } ( - 6 ) ^ { n } n ( x - 1 ) ^ { n - 1 }$
C) $6 \sum _ { n = 1 } ^ { \infty } ( - 1 ) ^ { n + 1 } n ( x - 1 ) ^ { n - 1 }$
D) $\sum _ { n = 0 } ^ { \infty } ( - 6 ) ^ { n - 1 } n ( x - 1 ) ^ { n }$
E) $\sum _ { n = 0 } ^ { \infty } ( - 6 ) ^ { n - 1 } n ( x - 1 ) ^ { n + 1 }$