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Question Number 4486 by Rasheed Soomro last updated on 31/Jan/16

f(x)=e^x (1−x^2 ) and the domain D(f) of  f  is chosen appropriately, find (d/dx)f(x)  at   any point x in D(f) .

$${f}\left({x}\right)={e}^{{x}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)\:{and}\:{the}\:{domain}\:{D}\left({f}\right)\:{of}\:\:{f} \\ $$$${is}\:{chosen}\:{appropriately},\:{find}\:\frac{{d}}{{dx}}{f}\left({x}\right)\:\:{at}\: \\ $$$${any}\:{point}\:{x}\:{in}\:{D}\left({f}\right)\:. \\ $$

Answered by Yozzii last updated on 31/Jan/16

((df(x))/dx)=e^x (1−x^2 )+e^x (−2x)=e^x (1−2x−x^2 )

$$\frac{{df}\left({x}\right)}{{dx}}={e}^{{x}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)+{e}^{{x}} \left(−\mathrm{2}{x}\right)={e}^{{x}} \left(\mathrm{1}−\mathrm{2}{x}−{x}^{\mathrm{2}} \right) \\ $$

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