2x^10y^6/4x^4y^8= eching

$$\frac { 2 x ^ { 10 } y ^ { 6 } } { 4 x ^ { 4 } y ^ { 8 } } =$$

Baholash

$$\frac{x^{6}}{2y^{2}}$$

Tartib xususiyati koeffitsientidan foydalanish qadamlari

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{2^{1}x^{10}y^{6}}{4^{1}x^{4}y^{8}}$$

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

$$\frac{2^{1}}{4^{1}}x^{10-4}y^{6-8}$$

10 dan 4 ni ayirish.

$$\frac{2^{1}}{4^{1}}x^{6}y^{6-8}$$

6 dan 8 ni ayirish.

$$\frac{2^{1}}{4^{1}}x^{6}y^{-2}$$

\frac{2}{4} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{1}{2}x^{6}\times \frac{1}{y^{2}}$$

x ga nisbatan hosilani topish

$$\frac{3x^{5}}{y^{2}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2y^{6}}{4y^{8}}x^{10-4})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2y^{2}}x^{6})$$

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

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

Arifmetik hisobni amalga oshirish.

$$\frac{3}{y^{2}}x^{5}$$