Originally Posted by

**Jones** Hi,

I have the following:

$\displaystyle y = Ate^{-2x}$

$\displaystyle y ^{\prime} = Ae^{-2x}-2Ate^{-2x}$

For $\displaystyle y^{\prime\prime}$ i seem to get different answers, depending on the method.

$\displaystyle \frac{d}{dx}f(x)\cdot g(x) = f^{\prime}(x)\cdot g(x) + f(x)\cdot g^{\prime}(x)$

1. $\displaystyle \frac{d}{dx}~Ae^{-2x}-2Ate^{-2x} = -2Ae^{-2x} + 4Ae^{-2x}$

2. If i factor out the e term. $\displaystyle \frac{d}{dx}~e^{-2x}\cdot (A-2At) = -2e^{-2x} \cdot (A-2At) + e^{-2x}\cdot -2A = -4Ae^{-2x} + 4Ate^{-2x}$

One of these is more correct than the other, which is it?