Answer
$f^{n}(x)$ = $(-1)^{n}{\frac{(2n+1)(2n-1)\times...3}{2^{n}}}x^{-\frac{(2n+3)}{2}}$
Work Step by Step
$f(x)$ = $x^{-\frac{3}{2}}$
$f'(x)$ = ${-\frac{3}{2}}x^{-\frac{5}{2}}$
$f''(x)$ = ${\frac{3\times5}{2^{2}}}x^{-\frac{7}{2}}$
$f'''(x)$ = ${-\frac{3\times5\times7}{2^{3}}}x^{-\frac{9}{2}}$
$f^{n}(x)$ = $(-1)^{n}{\frac{(2n+1)(2n-1)\times...3}{2^{n}}}x^{-\frac{(2n+3)}{2}}$
