# Math Help - Derivative of e.

1. ## Derivative of e.

Please check if i have done these correctly.

$f(x) = e^{-x^2}$

$f'(x) = -2xe^{-x^2}$

$f''(x)= -4x^2e^{-x^2} - 2e^{-x^2}$

Can i also write f''(x) as $-4e^{-x^2}x^2-2e^{-x^2}$ ??

2. Originally Posted by el123
Please check if i have done these correctly.

$f(x) = e^{-x^2}$

$f'(x) = -2xe^{-x^2}$

$f''(x)= -4x^2e^{-x^2} - 2e^{-x^2}$

Can i also write f''(x) as $-4e^{-x^2}x^2-2e^{-x^2}$ ??
Your $f''(x)$ is incorrect as it should be $4x^2e^{-x^2} - 2e^{-x^2}$ since we started with a factor of $-2x$ and multiplied it by $-2x$ again when we use the chain rule to get $-2x*-2x = 4x^2$. And as for your re-writing of $f''(x)$, you just moved the $x^2$ term around...that's not different in any meaningful way ie. just like $ax^2$ and $x^2a$ are obviously the same since multiplication in $\mathbb{R}$ is commutative. If you wish to factor $f''(x)$ you can rewrite it as $f''(x) = (4x - 2)e^{-x^2}$