3.4-bo'lim : Mahsulot va miqdor qoidasi
7. Agar\(f\left( 2 \right) = - 8\), \(f'\left( 2 \right) = 3\), \(g\left( 2 \right) = 17\) va \(g'\left( 2 \right) = - 4\) \({\left( {f\,g} \right)^\prime }\left( 2 \right)\) qiymatini aniqlaydi.
Yechim
Biz bilamizki, mahsulot qoidasi,
\[{\left( {f\,g} \right)^\prime }\left( x \right) = f'\left( x \right)g\left( x \right) + f\left( x \right)g'\left( x \right)\]Endi biz \(x = 2\)-da buning qiymatini bilmoqchimiz va shuning uchun biz qilishimiz kerak bo'lgan narsa buni lotinga ulashdir. Shunday qilib,
\[{\left( {f\,g} \right)^\prime }\left( 2 \right) = f'\left( 2 \right)g\left( 2 \right) + f\left( 2 \right)g'\left( 2 \right)\]Endi bizga ushbu miqdorlarning barchasi uchun qiymatlar berildi va shuning uchun biz qilishimiz kerak bo'lgan narsa ularni yuqoridagi "formulamiz" ga ulashdir.
\[{\left( {f\,g} \right)^\prime }\left( 2 \right) = \left( 3 \right)\left( {17} \right) + \left( { - 8} \right)\left( { - 4} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{83}}\]