Derivative of $-2e^{-x^2}x$ $$f(x) = -2e^{-x^2}x$$
Find $f'(x)$:
I have making a small  mistake some where in my calculation and I cannot find it.
The answer is stated as:
$$e^{-x^2}(4x^2-2)$$
However I got something different from my work:
$$f'(x)=-2[(e^{-x^2})'(x)+(e^{-x^2})(x)']$$
$$=-2[(e^{-x^2})(-2x)+e^{-x^2}]$$
$$=-2[-2xe^{-x^2}+e^{-x^2}]$$
$$=4xe^{-x^2}-2e^{-x^2}$$
$$=e^{-x^2}(4x-2)$$

(1) $f(x)=-2e^{-x^2}x$ (apply product rule)
(2) $-2 (e^{-x^2}(1)+x(e^{-x^2})\frac{d}{dx}(-x^2)$)
(3) $-2(e^{-x^2}-2x^2e^{-x^2})$  
(4) $-2e^{-x^2}+4x^2e^{-x^2}$
(5) $e^{-x^2}(4x^2-2)$
