y^frac{1{3}}*y^frac{3{5}} eching

$$y ^ { \frac { 1 } { 3 } } \cdot y ^ { \frac { 3 } { 5 } }$$

y ga nisbatan hosilani topish

$$\frac{14}{15\sqrt[15]{y}}$$

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.

$$\sqrt[3]{y}\frac{\mathrm{d}}{\mathrm{d}y}(y^{\frac{3}{5}})+y^{\frac{3}{5}}\frac{\mathrm{d}}{\mathrm{d}y}(\sqrt[3]{y})$$

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

$$\sqrt[3]{y}\times \frac{3}{5}y^{\frac{3}{5}-1}+y^{\frac{3}{5}}\times \frac{1}{3}y^{\frac{1}{3}-1}$$

Qisqartirish.

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

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

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

Qisqartirish.

$$\frac{3}{5}y^{-\frac{1}{15}}+\frac{1}{3}y^{-\frac{1}{15}}$$

Baholash

$$y^{\frac{14}{15}}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{1}{3} va \frac{3}{5} ni qo‘shib, \frac{14}{15} ni oling.

$$y^{\frac{14}{15}}$$