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Question Number 4992 by love math last updated on 29/Mar/16

f(x)=2x e^x   f ′(x) −?

$${f}\left({x}\right)=\mathrm{2}{x}\:{e}^{{x}} \\ $$$${f}\:'\left({x}\right)\:−? \\ $$

Answered by FilupSmith last updated on 29/Mar/16

f(x)=uv  f(x)=uv′+u′v    ∴f ′(x)=2e^x +2xe^x   f ′(x)=2e^x (x+1)

$${f}\left({x}\right)={uv} \\ $$$${f}\left({x}\right)={uv}'+{u}'{v} \\ $$$$ \\ $$$$\therefore{f}\:'\left({x}\right)=\mathrm{2}{e}^{{x}} +\mathrm{2}{xe}^{{x}} \\ $$$${f}\:'\left({x}\right)=\mathrm{2}{e}^{{x}} \left({x}+\mathrm{1}\right) \\ $$

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