# How do you differentiate f(x) = (sinx)/(e^(x-2)+x) using the quotient rule?

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