{x}^frac{1{3}}(x-4) eching

$${ x }^{ \frac{ 1 }{ 3 } } (x-4)$$

Baholash

$$\sqrt[3]{x}\left(x-4\right)$$

Yechim qadamlari

x^{\frac{1}{3}} ga x-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{\frac{1}{3}}x-4x^{\frac{1}{3}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{1}{3} va 1 ni qo‘shib, \frac{4}{3} ni oling.

$$x^{\frac{4}{3}}-4x^{\frac{1}{3}}$$

x ga nisbatan hosilani topish

$$\frac{4\left(x-1\right)}{3x^{\frac{2}{3}}}$$

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.

$$\sqrt[3]{x}\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-4)+\left(x^{1}-4\right)\frac{\mathrm{d}}{\mathrm{d}x}(\sqrt[3]{x})$$

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

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

Qisqartirish.

$$\sqrt[3]{x}x^{0}+\left(x^{1}-4\right)\times \frac{1}{3}x^{-\frac{2}{3}}$$

x^{1}-4 ni \frac{1}{3}x^{-\frac{2}{3}} marotabaga ko'paytirish.

$$\sqrt[3]{x}x^{0}+x^{1}\times \frac{1}{3}x^{-\frac{2}{3}}-4\times \frac{1}{3}x^{-\frac{2}{3}}$$

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

$$x^{\frac{1}{3}}+\frac{1}{3}x^{1-\frac{2}{3}}-4\times \frac{1}{3}x^{-\frac{2}{3}}$$

Qisqartirish.

$$\sqrt[3]{x}+\frac{1}{3}\sqrt[3]{x}-\frac{4}{3}x^{-\frac{2}{3}}$$