![\bf f(x)=e^{-x}(e^{2x}+x^2)\iff f(x)=e^{-x}e^{2x}+e^{-x}x^2 \\\\\\ f(x)=e^{2x-x}+\cfrac{x^2}{e^x}\implies f(x)=e^x+\cfrac{x^2}{e^x}\\\\ -----------------------------\\\\ \cfrac{dy}{dx}\left[ \cfrac{x^2}{e^x} \right]\implies \cfrac{2xe^x-x^2e^x}{(e^x)^2}\implies \cfrac{xe^x(2-x)}{(e^x)(e^x)}\implies \cfrac{x(2-x)}{e^x}\\\\ -----------------------------\\\\ \cfrac{dy}{dx}=e^x+\cfrac{x(2-x)}{e^x}](/tpl/images/0313/6829/e0403.png)
Find f'(x). anything !
also, bonus!
f(x)= e^(2x-1) + e^2
...
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