w^frac{4{7}}*w^frac{1{2}} eching

$$w ^ { \frac { 4 } { 7 } } \cdot w ^ { \frac { 1 } { 2 } }$$

w ga nisbatan hosilani topish

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

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.

$$w^{\frac{4}{7}}\frac{\mathrm{d}}{\mathrm{d}w}(\sqrt{w})+\sqrt{w}\frac{\mathrm{d}}{\mathrm{d}w}(w^{\frac{4}{7}})$$

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

$$w^{\frac{4}{7}}\times \frac{1}{2}w^{\frac{1}{2}-1}+\sqrt{w}\times \frac{4}{7}w^{\frac{4}{7}-1}$$

Qisqartirish.

$$w^{\frac{4}{7}}\times \frac{1}{2}w^{-\frac{1}{2}}+\sqrt{w}\times \frac{4}{7}w^{-\frac{3}{7}}$$

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

$$\frac{1}{2}w^{\frac{4}{7}-\frac{1}{2}}+\frac{4}{7}w^{\frac{1}{2}-\frac{3}{7}}$$

Qisqartirish.

$$\frac{1}{2}\sqrt[14]{w}+\frac{4}{7}\sqrt[14]{w}$$

Baholash

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