3.3-bo'lim : Farqlash formulalari
6. \(f\left( x \right) = 10\,\sqrt[5]{{{x^3}}} - \sqrt {{x^7}} + 6\,\sqrt[3]{{{x^8}}} - 3\) ning hosilasini toping.
Yechim
Bu erda biz ushbu bo'limda muhokama qilgan qoidalardan foydalanib lotinni olishdan boshqa ko'p ish yo'q.
Esda tutingki, hosila olishni boshlashdan oldin siz ildizlarni kasr ko'rsatkichlariga aylantirishingiz kerak. Mana qayta yozilgan funksiya.
\[f\left( x \right) = 10\,{\left( {{x^3}} \right)^{\frac{1}{5}}} - {\left( {{x^7}} \right)^{\frac{1}{2}}} + 6{\left( {{x^8}} \right)^{\frac{1}{3}}} - 3 = 10\,{x^{\frac{3}{5}}} - {x^{\frac{7}{2}}} + 6{x^{\frac{8}{3}}} - 3\]hosilasi,
\[f'\left( x \right) = 10\,\left( {\frac{3}{5}} \right){x^{ - \,\,\frac{2}{5}}} - \frac{7}{2}{x^{\frac{5}{2}}} + 6\left( {\frac{8}{3}} \right){x^{\frac{5}{3}}} = \require{bbox} \bbox[2pt,border:1px solid black]{{6{x^{ - \,\,\frac{2}{5}}} - \frac{7}{2}{x^{\frac{5}{2}}} + 16{x^{\frac{5}{3}}}}}\]