Question Number 4992 by love math last updated on 29/Mar/16
$${f}\left({x}\right)=\mathrm{2}{x}\:{e}^{{x}} \\ $$$${f}\:'\left({x}\right)\:−? \\ $$
Answered by FilupSmith last updated on 29/Mar/16
$${f}\left({x}\right)={uv} \\ $$$${f}\left({x}\right)={uv}'+{u}'{v} \\ $$$$ \\ $$$$\therefore{f}\:'\left({x}\right)=\mathrm{2}{e}^{{x}} +\mathrm{2}{xe}^{{x}} \\ $$$${f}\:'\left({x}\right)=\mathrm{2}{e}^{{x}} \left({x}+\mathrm{1}\right) \\ $$