{x}^frac{4{5}}(x+4) eching

$${ x }^{ \frac{ 4 }{ 5 } } (x+4)$$

Baholash

$$x^{\frac{4}{5}}\left(x+4\right)$$

Yechim qadamlari

x^{\frac{4}{5}} ga x+4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$x^{\frac{4}{5}}x+4x^{\frac{4}{5}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{4}{5} va 1 ni qo‘shib, \frac{9}{5} ni oling.

$$x^{\frac{9}{5}}+4x^{\frac{4}{5}}$$

x ga nisbatan hosilani topish

$$\frac{9x+16}{5\sqrt[5]{x}}$$

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.

$$x^{\frac{4}{5}}\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}+4)+\left(x^{1}+4\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{4}{5}})$$

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

$$x^{\frac{4}{5}}x^{1-1}+\left(x^{1}+4\right)\times \frac{4}{5}x^{\frac{4}{5}-1}$$

Qisqartirish.

$$x^{\frac{4}{5}}x^{0}+\left(x^{1}+4\right)\times \frac{4}{5}x^{-\frac{1}{5}}$$

x^{1}+4 ni \frac{4}{5}x^{-\frac{1}{5}} marotabaga ko'paytirish.

$$x^{\frac{4}{5}}x^{0}+x^{1}\times \frac{4}{5}x^{-\frac{1}{5}}+4\times \frac{4}{5}x^{-\frac{1}{5}}$$

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

$$x^{\frac{4}{5}}+\frac{4}{5}x^{1-\frac{1}{5}}+4\times \frac{4}{5}x^{-\frac{1}{5}}$$

Qisqartirish.

$$x^{\frac{4}{5}}+\frac{4}{5}x^{\frac{4}{5}}+\frac{16}{5}x^{-\frac{1}{5}}$$