\[ f(x) = e^{-x} \] First 3 derivatives
\[ e^{-x} = -e^{-x} + e^{-x} + -e^{-x} + ...\] \[ e^{-x} = \frac {1}{0!}x^{0} + \frac {-1}{1!}x^{1} + \frac {1}{2!}x^{2} + \frac {-1}{3!}x^{3}\] \[ e^{-x} = 1 - x + \frac {1}{2}x^{2} - \frac {1}{6}x^{3}\]