If we write a function $y$ as a power series $y={\displaystyle \underset{n=0}{\overset{}{}}}{a}_n{x}^n,$ which of the following would represent $y^{\text{'}}?$

$y^{\text{'}}={\displaystyle \underset{n=0}{\overset{}{}}}{a}_{n}n{x}^n$

$y^{\text{'}}={\displaystyle \underset{n=0}{\overset{}{}}}{a}_{n}n(n-1)x^{n-2}$

$y^{\text{'}}={\displaystyle \underset{n=0}{\overset{}{}}}{a}_n{x}^n$

$y^{\text{'}}={\displaystyle \underset{n=0}{\overset{}{}}}{a}_{n}n{x}^{n-1}$

Which of the following would represent $y^{\text{'}\text{'}}?$

$y^{\text{'}\text{'}}={\displaystyle \underset{n=0}{\overset{}{}}}{a}_{n}n{x}^n$

$y^{\text{'}\text{'}}={\displaystyle \underset{n=0}{\overset{}{}}}{a}_{n}n(n-1)x^{n-2}$

$y^{\text{'}\text{'}}={\displaystyle \underset{n=0}{\overset{}{}}}{a}_n{x}^n$

$y^{\text{'}\text{'}}={\displaystyle \underset{n=0}{\overset{}{}}}{a}_{n}n{x}^{n-1}$