Chapter 3 - Differentiation - 3.5 Higher Derivatives - Exercises - Page 136: 35

$f^{n}(x)$ = $(-1)^{n}(x-n)e^{-x}$

$f(x)$ = $x{e^{-x}}$ $f'(x)$ = $-x{e^{-x}}+e^{-x}$ = $-(x-1)e^{-x}$ $f''(x)$ = $(x-1)e^{-x}-e^{-x}$ = $(x-2)e^{-x}$ $f'''(x)$ = $-(x-2)e^{-x}+e^{-x}$ = $-(x-3)e^{-x}$ $f^{n}(x)$ = $(-1)^{n}(x-n)e^{-x}$