u^frac{5{8}}*u^frac{1{2}} eching

$$u ^ { \frac { 5 } { 8 } } \cdot u ^ { \frac { 1 } { 2 } }$$

u ga nisbatan hosilani topish

$$\frac{9\sqrt[8]{u}}{8}$$

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.

$$u^{\frac{5}{8}}\frac{\mathrm{d}}{\mathrm{d}u}(\sqrt{u})+\sqrt{u}\frac{\mathrm{d}}{\mathrm{d}u}(u^{\frac{5}{8}})$$

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

$$u^{\frac{5}{8}}\times \frac{1}{2}u^{\frac{1}{2}-1}+\sqrt{u}\times \frac{5}{8}u^{\frac{5}{8}-1}$$

Qisqartirish.

$$u^{\frac{5}{8}}\times \frac{1}{2}u^{-\frac{1}{2}}+\sqrt{u}\times \frac{5}{8}u^{-\frac{3}{8}}$$

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

$$\frac{1}{2}u^{\frac{5}{8}-\frac{1}{2}}+\frac{5}{8}u^{\frac{1}{2}-\frac{3}{8}}$$

Qisqartirish.

$$\frac{1}{2}\sqrt[8]{u}+\frac{5}{8}\sqrt[8]{u}$$

Baholash

$$u^{\frac{9}{8}}$$