Question Number 11914 by ahmet last updated on 04/Apr/17
$${Turevlenebilir}\:{bir}\:{f}\:{fonksiyonu}\:{icin} \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left({y}\right)+\mathrm{2}{xy}\:{ve}\:{f}'\left(\mathrm{0}\right)=−\mathrm{3} \\ $$$${old}.{gore}\:{f}'\left(\mathrm{2}\right)=? \\ $$$${czm}\because\:\:{f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left({y}\right)+\mathrm{2}{xy} \\ $$$${y}\:{yi}\:{sabit}\:{kabul}\:{edersek} \\ $$$${f}'\left({x}+{y}\right)={f}'\left({x}\right)+\mathrm{2}{y} \\ $$$${x}=\mathrm{0},{y}=\mathrm{2}\:{icn} \\ $$$${f}'\left(\mathrm{2}\right)={f}'\left(\mathrm{0}\right)+\mathrm{2}.\mathrm{2} \\ $$$${f}'\left(\mathrm{2}\right)=−\mathrm{3}+\mathrm{4}=\mathrm{1} \\ $$