v^-1/3v^6/5 eching

$$v ^ { - 1 / 3 } v ^ { 6 / 5 }$$

v ga nisbatan hosilani topish

$$\frac{13}{15v^{\frac{2}{15}}}$$

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.

$$v^{-\frac{1}{3}}\frac{\mathrm{d}}{\mathrm{d}v}(v^{\frac{6}{5}})+v^{\frac{6}{5}}\frac{\mathrm{d}}{\mathrm{d}v}(v^{-\frac{1}{3}})$$

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

$$v^{-\frac{1}{3}}\times \frac{6}{5}v^{\frac{6}{5}-1}+v^{\frac{6}{5}}\left(-\frac{1}{3}\right)v^{-\frac{1}{3}-1}$$

Qisqartirish.

$$v^{-\frac{1}{3}}\times \frac{6}{5}\sqrt[5]{v}+v^{\frac{6}{5}}\left(-\frac{1}{3}\right)v^{-\frac{4}{3}}$$

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

$$\frac{6}{5}v^{-\frac{1}{3}+\frac{1}{5}}-\frac{1}{3}v^{\frac{6}{5}-\frac{4}{3}}$$

Qisqartirish.

$$\frac{6}{5}v^{-\frac{2}{15}}-\frac{1}{3}v^{-\frac{2}{15}}$$

Baholash

$$v^{\frac{13}{15}}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -\frac{1}{3} va \frac{6}{5} ni qo‘shib, \frac{13}{15} ni oling.

$$v^{\frac{13}{15}}$$