49y^6/56y^2 eching

$$\frac { 49 y ^ { 6 } } { 56 y ^ { 2 } }$$

Baholash

$$\frac{7y^{4}}{8}$$

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\left(49y^{6}\right)^{1}\times \frac{1}{56y^{2}}$$

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

$$49^{1}\left(y^{6}\right)^{1}\times \frac{1}{56}\times \frac{1}{y^{2}}$$

Ko'paytirishning kommutativ xususiyatidan foydalanish.

$$49^{1}\times \frac{1}{56}\left(y^{6}\right)^{1}\times \frac{1}{y^{2}}$$

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

$$49^{1}\times \frac{1}{56}y^{6}y^{2\left(-1\right)}$$

2 ni -1 marotabaga ko'paytirish.

$$49^{1}\times \frac{1}{56}y^{6}y^{-2}$$

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

$$49^{1}\times \frac{1}{56}y^{6-2}$$

6 va -2 belgilarini qo'shish.

$$49^{1}\times \frac{1}{56}y^{4}$$

49 ni 1 daraja ko'rsatgichiga oshirish.

$$49\times \frac{1}{56}y^{4}$$

49 ni \frac{1}{56} marotabaga ko'paytirish.

$$\frac{7}{8}y^{4}$$

Eksponent koeffitsienti uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{49^{1}y^{6}}{56^{1}y^{2}}$$

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

$$\frac{49^{1}y^{6-2}}{56^{1}}$$

6 dan 2 ni ayirish.

$$\frac{49^{1}y^{4}}{56^{1}}$$

\frac{49}{56} ulushini 7 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{7}{8}y^{4}$$

y ga nisbatan hosilani topish

$$\frac{7y^{3}}{2}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{49}{56}y^{6-2})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{7}{8}y^{4})$$

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

$$4\times \frac{7}{8}y^{4-1}$$

Arifmetik hisobni amalga oshirish.

$$\frac{7}{2}y^{3}$$