$\displaystyle f(x)=\frac{14x}{(1+12.6e^{-0.73x})}$

Hello, I'm having some brain freeze on finding the derivative for this problem.

First, I changed the denominator to $\displaystyle {(1+12.6e^{-0.73x})^{-1}$, and then used the Product Rule. $\displaystyle f(x)=\frac{d}{dx}{[14x]}*{(1+12.6e^{-0.73x})^{-1}+\frac{d}{dx}{[(1+12.6e^{-0.73x})^{-1}]*{14x}$

That left me with: $\displaystyle f(x)={[14]}*{(1+12.6e^{-0.73x})^{-1}+{[(12.6e^{-0.73x})^{-1}]*{14x}$

This is where I'm getting brain frozen. I checked the back off the book it says the answer is: $\displaystyle f(x)={[14]}*{(1+12.6e^{-0.73x})^{-1}+ {128.772x(1+12.6e^{-0.73x})^{-2}e^{-0.73x}$.

I'm not sure where the value of $\displaystyle {128.772x(1+12.6e^{-0.73x})^{-2}e^{-0.73x}$ came from. I see parts of the Chain Rule, but the 128.772 has me dumbfounded. If there's a coefficient in front of $\displaystyle {e}$ what happens when taking the derivative of $\displaystyle {e}^{x}$?