Expansion of function into power series of X How to expand f (x) = D ((e ^ x-1) / x) / DX into a power series and what is the specific process?

Expansion of function into power series of X How to expand f (x) = D ((e ^ x-1) / x) / DX into a power series and what is the specific process?

Expand by Taylor series e ^ x = 1 + X + x ^ 2 / 2 +... + (x ^ n) / (n!) (n from 0 to infinity)
{e ^ X-1 = x + x ^ 2 / 2 + x ^ 3 / 6 +... + (x ^ n) / (n!) (n from 0 to infinity)
(e ^ x-1) / x = 1 + X / 2 + x ^ 2 / 6 +.. + [x ^ (n-1)] / (n!) (n from 1 to infinity)
The derivation of F (x) = 1 / 2 + 1 / 3x +... + (n-1) / (n!) x ^ (n-2) (n from 2 to infinity)
Is the power series ∑ (n-1) / (n!) x ^ (n-2) (n from 2 to infinity)