Question Number 4486 by Rasheed Soomro last updated on 31/Jan/16
$${f}\left({x}\right)={e}^{{x}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)\:{and}\:{the}\:{domain}\:{D}\left({f}\right)\:{of}\:\:{f} \\ $$$${is}\:{chosen}\:{appropriately},\:{find}\:\frac{{d}}{{dx}}{f}\left({x}\right)\:\:{at}\: \\ $$$${any}\:{point}\:{x}\:{in}\:{D}\left({f}\right)\:. \\ $$
Answered by Yozzii last updated on 31/Jan/16
$$\frac{{df}\left({x}\right)}{{dx}}={e}^{{x}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)+{e}^{{x}} \left(−\mathrm{2}{x}\right)={e}^{{x}} \left(\mathrm{1}−\mathrm{2}{x}−{x}^{\mathrm{2}} \right) \\ $$