7v^2/42v^3 eching

$$\frac { 7 v ^ { 2 } } { 42 v ^ { 3 } }$$

Baholash

$$\frac{1}{6v}$$

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\left(7v^{2}\right)^{1}\times \frac{1}{42v^{3}}$$

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

$$7^{1}\left(v^{2}\right)^{1}\times \frac{1}{42}\times \frac{1}{v^{3}}$$

Ko'paytirishning kommutativ xususiyatidan foydalanish.

$$7^{1}\times \frac{1}{42}\left(v^{2}\right)^{1}\times \frac{1}{v^{3}}$$

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

$$7^{1}\times \frac{1}{42}v^{2}v^{3\left(-1\right)}$$

3 ni -1 marotabaga ko'paytirish.

$$7^{1}\times \frac{1}{42}v^{2}v^{-3}$$

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

$$7^{1}\times \frac{1}{42}v^{2-3}$$

2 va -3 belgilarini qo'shish.

$$7^{1}\times \frac{1}{42}\times \frac{1}{v}$$

7 ni 1 daraja ko'rsatgichiga oshirish.

$$7\times \frac{1}{42}\times \frac{1}{v}$$

7 ni \frac{1}{42} marotabaga ko'paytirish.

$$\frac{1}{6}\times \frac{1}{v}$$

Eksponent koeffitsienti uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{7^{1}v^{2}}{42^{1}v^{3}}$$

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

$$\frac{7^{1}v^{2-3}}{42^{1}}$$

2 dan 3 ni ayirish.

$$\frac{7^{1}\times \frac{1}{v}}{42^{1}}$$

\frac{7}{42} ulushini 7 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{6}\times \frac{1}{v}$$

v ga nisbatan hosilani topish

$$-\frac{1}{6v^{2}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{7}{42}v^{2-3})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{1}{6}\times \frac{1}{v})$$

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

$$-\frac{1}{6}v^{-1-1}$$

Arifmetik hisobni amalga oshirish.

$$-\frac{1}{6}v^{-2}$$