# How do you differentiate f(x)= (x-e^(x))/(e^x-3x) using the quotient rule?

$f ' \left(x\right) = \frac{2 {e}^{x} \cdot \left(x - 1\right)}{{e}^{x} - 3 x} ^ 2$
$f ' \left(x\right) = \frac{\left(1 - {e}^{x}\right) \left({e}^{x} - 3 x\right) - \left(x - {e}^{x}\right) \left({e}^{x} + 3\right)}{{e}^{x} - 3 x} ^ 2$
$f ' \left(x\right) = \frac{2 {e}^{x} \left(x - 1\right)}{{e}^{x} - 3 x} ^ 2$