15n/30n^3 eching

$$\frac { 15 n } { 30 n ^ { 3 } }$$

Baholash

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

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\left(15n^{1}\right)^{1}\times \frac{1}{30n^{3}}$$

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

$$15^{1}\left(n^{1}\right)^{1}\times \frac{1}{30}\times \frac{1}{n^{3}}$$

Ko'paytirishning kommutativ xususiyatidan foydalanish.

$$15^{1}\times \frac{1}{30}\left(n^{1}\right)^{1}\times \frac{1}{n^{3}}$$

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

$$15^{1}\times \frac{1}{30}n^{1}n^{3\left(-1\right)}$$

3 ni -1 marotabaga ko'paytirish.

$$15^{1}\times \frac{1}{30}n^{1}n^{-3}$$

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

$$15^{1}\times \frac{1}{30}n^{1-3}$$

1 va -3 belgilarini qo'shish.

$$15^{1}\times \frac{1}{30}n^{-2}$$

15 ni 1 daraja ko'rsatgichiga oshirish.

$$15\times \frac{1}{30}n^{-2}$$

15 ni \frac{1}{30} marotabaga ko'paytirish.

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

Eksponent koeffitsienti uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{15^{1}n^{1}}{30^{1}n^{3}}$$

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

$$\frac{15^{1}n^{1-3}}{30^{1}}$$

1 dan 3 ni ayirish.

$$\frac{15^{1}n^{-2}}{30^{1}}$$

\frac{15}{30} ulushini 15 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

n ga nisbatan hosilani topish

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

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{15}{30}n^{1-3})$$

Arifmetik hisobni amalga oshirish.

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

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

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

Arifmetik hisobni amalga oshirish.

$$-n^{-3}$$