# How do you find the derivative of (2x)/(3+e^x)?

Mar 7, 2018

$\frac{6 + 2 {e}^{x} - 2 x {e}^{x}}{3 + {e}^{x}} ^ 2$

#### Explanation:

We can use quotient rule:

$\frac{d}{\mathrm{dx}} \left(\frac{f}{g}\right) = \frac{g f ' - f g '}{g} ^ 2$

If $f \left(x\right) = 2 x$ and $g \left(x\right) = 3 + {e}^{x}$, the derivative is

$\frac{2 \left(3 + {e}^{x}\right) - 2 x \left({e}^{x}\right)}{3 + {e}^{x}} ^ 2 = \frac{6 + 2 {e}^{x} - 2 x {e}^{x}}{3 + {e}^{x}} ^ 2$