u^frac{1{8}}*u^frac{3{4}} eching

$$u ^ { \frac { 1 } { 8 } } \cdot u ^ { \frac { 3 } { 4 } }$$

u ga nisbatan hosilani topish

$$\frac{7}{8\sqrt[8]{u}}$$

Koʻpaytma uchun derivativ qoidasidan foydalanish qadamlari

Har qanday ikki differensial funksiya uchun, ikki funksiya koʻpaytmasining hosilasi birinchi funksiya marotabasi, ikkinchi plyus hosilasi ikkinchi funksiya marotabasi birinchining hosilasidir.

$$\sqrt[8]{u}\frac{\mathrm{d}}{\mathrm{d}u}(u^{\frac{3}{4}})+u^{\frac{3}{4}}\frac{\mathrm{d}}{\mathrm{d}u}(\sqrt[8]{u})$$

Polinomialning hosilasi bu uning shartlari hosilasining yig‘indisiga teng. Konstant shartning hosilasi 0. ax^{n} ning hosilasi nax^{n-1}.

$$\sqrt[8]{u}\times \frac{3}{4}u^{\frac{3}{4}-1}+u^{\frac{3}{4}}\times \frac{1}{8}u^{\frac{1}{8}-1}$$

Qisqartirish.

$$\sqrt[8]{u}\times \frac{3}{4}u^{-\frac{1}{4}}+u^{\frac{3}{4}}\times \frac{1}{8}u^{-\frac{7}{8}}$$

Ayni daraja ko'rsatkichlarini ko'paytirish uchun ularning darajalarini qo'shing.

$$\frac{3}{4}u^{\frac{1}{8}-\frac{1}{4}}+\frac{1}{8}u^{\frac{3}{4}-\frac{7}{8}}$$

Qisqartirish.

$$\frac{3}{4}u^{-\frac{1}{8}}+\frac{1}{8}u^{-\frac{1}{8}}$$

Baholash

$$u^{\frac{7}{8}}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{1}{8} va \frac{3}{4} ni qo‘shib, \frac{7}{8} ni oling.

$$u^{\frac{7}{8}}$$