Find the first five derivatives. Use the pattern to find the $f^{(100)}(x)$ and the $f^{(n)}(x).($Hint: Do NOT multiply numbers to see the pattern.$)$

$f(x)=\frac{1}{x}$

$f^{\text{'}}(x)=$

$f^{\text{'}}(x)=$

$f^{\text{'}\text{'}}(x)=$

$f^{(4)}(x)=$

$f^{(5)}(x)=$

$f^{(n)}(x)=$