Biz \(g\left( x \right)\) nima ekanligini bilmasak ham, bizda ikkita funktsiya mahsuloti mavjud va shuning uchun biz \(f\left( x \right)\) hosilasini aniqlash uchun mahsulot qoidasidan foydalanishimiz mumkin.

\[f'\left( x \right) = 3{x^2}g\left( x \right) + {x^3}g'\left( x \right)\] Endi biz qilishimiz kerak bo'lgan yagona narsa \(x = - 7\)-ni unga ulash va \(f'\left( { - 7} \right)\) qiymatini aniqlash uchun berilgan ma'lumotlardan foydalanish.

\[f'\left( { - 7} \right) = 3{\left( { - 7} \right)^2}g\left( { - 7} \right) + {\left( { - 7} \right)^3}g'\left( { - 7} \right) = 3\left( {49} \right)\left( 2 \right) + \left( { - 343} \right)\left( { - 9} \right) = \require{bbox} \bbox[2pt,border:1px solid black]{{3381}}\]