find the derivative of f(x)=2e^-(x-4)^2

[twinmom]

I'm having trouble taking the derivative of f(x)=2e^-(x-4)^2.
My solution ends up being -2(x-4)^2e^(-x-4)^2. What I'm doing is trying to find the local extrema of this function and I'm getting stuck at the derivative. Any thoughts?

 

[galactus]

Almost. You've got one small error.

\(\displaystyle \L\\\frac{d}{dx}[2e^{-(x-4)^{2}}]\)

Let \(\displaystyle u=x-4\)

\(\displaystyle \L\\\frac{d}{dx}[2e^{-u^{2}}]={-}4ue^{-u^{2}}\)


\(\displaystyle \L\\\underbrace{{-}4}_{\uparrow}_{\text{not -2}}(x-4)e^{-(x-4)^{2}}\)

You can rearrange this most any way you wish.