3n/2n^2 eching

$$\frac { 3 n } { 2 n ^ { 2 } }$$

Baholash

$$\frac{3}{2n}$$

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\left(3n^{1}\right)^{1}\times \frac{1}{2n^{2}}$$

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

$$3^{1}\left(n^{1}\right)^{1}\times \frac{1}{2}\times \frac{1}{n^{2}}$$

Ko'paytirishning kommutativ xususiyatidan foydalanish.

$$3^{1}\times \frac{1}{2}\left(n^{1}\right)^{1}\times \frac{1}{n^{2}}$$

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

$$3^{1}\times \frac{1}{2}n^{1}n^{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$3^{1}\times \frac{1}{2}n^{1}n^{-2}$$

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

$$3^{1}\times \frac{1}{2}n^{1-2}$$

1 va -2 belgilarini qo'shish.

$$3^{1}\times \frac{1}{2}\times \frac{1}{n}$$

3 ni 1 daraja ko'rsatgichiga oshirish.

$$3\times \frac{1}{2}\times \frac{1}{n}$$

3 ni \frac{1}{2} marotabaga ko'paytirish.

$$\frac{3}{2}\times \frac{1}{n}$$

Eksponent koeffitsienti uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{3^{1}n^{1}}{2^{1}n^{2}}$$

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

$$\frac{3^{1}n^{1-2}}{2^{1}}$$

1 dan 2 ni ayirish.

$$\frac{3^{1}\times \frac{1}{n}}{2^{1}}$$

3 ni 2 ga bo'lish.

$$\frac{3}{2}\times \frac{1}{n}$$

n ga nisbatan hosilani topish

$$-\frac{3}{2n^{2}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{3}{2}n^{1-2})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{3}{2}\times \frac{1}{n})$$

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

$$-\frac{3}{2}n^{-1-1}$$

Arifmetik hisobni amalga oshirish.

$$-\frac{3}{2}n^{-2}$$