D^frac{2{5}}*D^frac{1{5}} eching

$$D ^ { \frac { 2 } { 5 } } \cdot D ^ { \frac { 1 } { 5 } }$$

D ga nisbatan hosilani topish

$$\frac{3}{5D^{\frac{2}{5}}}$$

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.

$$D^{\frac{2}{5}}\frac{\mathrm{d}}{\mathrm{d}D}(\sqrt[5]{D})+\sqrt[5]{D}\frac{\mathrm{d}}{\mathrm{d}D}(D^{\frac{2}{5}})$$

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

$$D^{\frac{2}{5}}\times \frac{1}{5}D^{\frac{1}{5}-1}+\sqrt[5]{D}\times \frac{2}{5}D^{\frac{2}{5}-1}$$

Qisqartirish.

$$D^{\frac{2}{5}}\times \frac{1}{5}D^{-\frac{4}{5}}+\sqrt[5]{D}\times \frac{2}{5}D^{-\frac{3}{5}}$$

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

$$\frac{1}{5}D^{\frac{2-4}{5}}+\frac{2}{5}D^{\frac{1-3}{5}}$$

Qisqartirish.

$$\frac{1}{5}D^{-\frac{2}{5}}+\frac{2}{5}D^{-\frac{2}{5}}$$

Baholash

$$D^{\frac{3}{5}}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{2}{5} va \frac{1}{5} ni qo‘shib, \frac{3}{5} ni oling.

$$D^{\frac{3}{5}}$$