22y^6z^8/zyz^-7 eching

$$\frac { 22 y ^ { 6 } z ^ { 8 } } { z y z ^ { - 7 } }$$

Baholash

$$22y^{5}z^{14}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va -7 ni qo‘shib, -6 ni oling.

$$\frac{22y^{6}z^{8}}{z^{-6}y}$$

Surat va maxrajdagi ikkala y ni qisqartiring.

$$\frac{22y^{5}z^{8}}{z^{-6}}$$

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

$$22y^{5}z^{14}$$

y ga nisbatan hosilani topish

$$110y^{4}z^{14}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{22z^{8}z^{7}}{z}y^{6-1})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}y}(22z^{14}y^{5})$$

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

$$5\times 22z^{14}y^{5-1}$$

Arifmetik hisobni amalga oshirish.

$$110z^{14}y^{4}$$