3n^-1/5n^-4 eching

$$\frac { 3 n ^ { - 1 } } { 5 n ^ { - 4 } }$$

Baholash

$$\frac{3n^{3}}{5}$$

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\left(3\times \frac{1}{n}\right)^{1}\times \frac{1}{5n^{-4}}$$

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

$$3^{1}\times \left(\frac{1}{n}\right)^{1}\times \frac{1}{5}\times \frac{1}{n^{-4}}$$

Ko'paytirishning kommutativ xususiyatidan foydalanish.

$$3^{1}\times \frac{1}{5}\times \left(\frac{1}{n}\right)^{1}\times \frac{1}{n^{-4}}$$

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

$$3^{1}\times \frac{1}{5}\times \frac{1}{n}n^{-4\left(-1\right)}$$

-4 ni -1 marotabaga ko'paytirish.

$$3^{1}\times \frac{1}{5}\times \frac{1}{n}n^{4}$$

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

$$3^{1}\times \frac{1}{5}n^{-1+4}$$

-1 va 4 belgilarini qo'shish.

$$3^{1}\times \frac{1}{5}n^{3}$$

3 ni 1 daraja ko'rsatgichiga oshirish.

$$3\times \frac{1}{5}n^{3}$$

3 ni \frac{1}{5} marotabaga ko'paytirish.

$$\frac{3}{5}n^{3}$$

n ga nisbatan hosilani topish

$$\frac{9n^{2}}{5}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{3}{5}n^{-1-\left(-4\right)})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{3}{5}n^{3})$$

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

$$3\times \frac{3}{5}n^{3-1}$$

Arifmetik hisobni amalga oshirish.

$$\frac{9}{5}n^{2}$$