8y^7z^6/4y^6z^5 eching

$$\frac { 8 y ^ { 7 } z ^ { 6 } } { 4 y ^ { 6 } z ^ { 5 } }$$

Baholash

$$2yz$$

Tartib xususiyati koeffitsientidan foydalanish qadamlari

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{8^{1}y^{7}z^{6}}{4^{1}y^{6}z^{5}}$$

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

$$\frac{8^{1}}{4^{1}}y^{7-6}z^{6-5}$$

7 dan 6 ni ayirish.

$$\frac{8^{1}}{4^{1}}y^{1}z^{6-5}$$

6 dan 5 ni ayirish.

$$\frac{8^{1}}{4^{1}}yz^{1}$$

8 ni 4 ga bo'lish.

$$2yz$$

y ga nisbatan hosilani topish

$$2z$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{8z^{6}}{4z^{5}}y^{7-6})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}y}(2zy^{1})$$

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

$$2zy^{1-1}$$

Arifmetik hisobni amalga oshirish.

$$2zy^{0}$$

Har qanday t sharti uchun (0 bundan mustasno) t^{0}=1.

$$2z\times 1$$

Har qanday t sharti uchun t\times 1=t va 1t=t.

$$2z$$