# How do you differentiate f(x)= e^x/(e^(-x) -x ) using the quotient rule?

$f ' \left(x\right) = \frac{2 - x \cdot {e}^{x} + {e}^{x}}{{e}^{- x} - x} ^ 2$
$f ' \left(x\right) = \frac{{e}^{x} \left({e}^{- x} - x\right) - {e}^{x} \left(- {e}^{- x} - 1\right)}{{e}^{- x} - x} ^ 2$ Expanding and collect equal Terms we get the result above.