4n^-1/n eching

$$\frac { 4 n ^ { - 1 } } { n }$$

n ga nisbatan hosilani topish

$$-\frac{8}{n^{3}}$$

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.

$$4\times \frac{1}{n}\frac{\mathrm{d}}{\mathrm{d}n}(\frac{1}{n})+\frac{1}{n}\frac{\mathrm{d}}{\mathrm{d}n}(4\times \frac{1}{n})$$

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

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

Qisqartirish.

$$4\times \frac{1}{n}\left(-1\right)n^{-2}+\frac{1}{n}\left(-4\right)n^{-2}$$

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

$$-4n^{-1-2}-4n^{-1-2}$$

Qisqartirish.

$$-4n^{-3}-4n^{-3}$$

O'xshash hadlarni birlashtirish.

$$\left(-4-4\right)n^{-3}$$

-4 ni -4 ga qo'shish.

$$-8n^{-3}$$

Yechim qadamlari

Ayni asosning daraja ko'rsatkichi bo'lish uchun maxrajning darajasini surat darajasidan bo'ling.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{4}{1}n^{-1-1})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}n}(4n^{-2})$$

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

$$-2\times 4n^{-2-1}$$

Arifmetik hisobni amalga oshirish.

$$-8n^{-3}$$

Baholash

$$\frac{4}{n^{2}}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun suratning darajasini maxraj darajasiga bo‘ling.

$$\frac{4}{n^{2}}$$