6u^-1/3u^8 eching

$$\frac { 6 u ^ { - 1 } } { 3 u ^ { 8 } }$$

Baholash

$$\frac{2}{u^{9}}$$

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\left(6\times \frac{1}{u}\right)^{1}\times \frac{1}{3u^{8}}$$

Ikki yoki undan ko'p raqam koʻpaytmasini daraja ko'rsatkichiga oshirish uchun har bir raqamni daraja ko'rsatkichiga oshiring va ularning koʻpaytmasini chiqaring.

$$6^{1}\times \left(\frac{1}{u}\right)^{1}\times \frac{1}{3}\times \frac{1}{u^{8}}$$

Ko'paytirishning kommutativ xususiyatidan foydalanish.

$$6^{1}\times \frac{1}{3}\times \left(\frac{1}{u}\right)^{1}\times \frac{1}{u^{8}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring.

$$6^{1}\times \frac{1}{3}\times \frac{1}{u}u^{8\left(-1\right)}$$

8 ni -1 marotabaga ko'paytirish.

$$6^{1}\times \frac{1}{3}\times \frac{1}{u}u^{-8}$$

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

$$6^{1}\times \frac{1}{3}u^{-1-8}$$

-1 va -8 belgilarini qo'shish.

$$6^{1}\times \frac{1}{3}u^{-9}$$

6 ni 1 daraja ko'rsatgichiga oshirish.

$$6\times \frac{1}{3}u^{-9}$$

6 ni \frac{1}{3} marotabaga ko'paytirish.

$$2u^{-9}$$

u ga nisbatan hosilani topish

$$-\frac{18}{u^{10}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}u}(\frac{6}{3}u^{-1-8})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}u}(2u^{-9})$$

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

$$-9\times 2u^{-9-1}$$

Arifmetik hisobni amalga oshirish.

$$-18u^{-10}$$