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

$\frac{d}{\mathrm{dx}} f \left(x\right) = \frac{\left[\left(2 {e}^{2 x} - x\right) \cdot {e}^{x}\right] - \left[{e}^{x} \cdot \left(4 {e}^{2 x} - 1\right)\right]}{2 {e}^{2 x} - x} ^ 2$
$\frac{d}{\mathrm{dx}} f \left(x\right) = \frac{\left[\left(2 {e}^{2 x} - x\right) \cdot {e}^{x}\right] - \left[{e}^{x} \cdot \left(4 {e}^{2 x} - 1\right)\right]}{2 {e}^{2 x} - x} ^ 2$