2x^3y/2xy^3 eching

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

Baholash

$$\left(\frac{x}{y}\right)^{2}$$

Tartib xususiyati koeffitsientidan foydalanish qadamlari

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\frac{2^{1}x^{3}y^{1}}{2^{1}x^{1}y^{3}}$$

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

$$2^{1-1}x^{3-1}y^{1-3}$$

1 dan 1 ni ayirish.

$$2^{0}x^{3-1}y^{1-3}$$

Har qanday a raqami uchun (0 bundan mustasno) a^{0}=1.

$$x^{3-1}y^{1-3}$$

3 dan 1 ni ayirish.

$$x^{2}y^{1-3}$$

1 dan 3 ni ayirish.

$$x^{2}y^{-2}$$

x ga nisbatan hosilani topish

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

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2y}{2y^{3}}x^{3-1})$$

Arifmetik hisobni amalga oshirish.

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

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

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

Arifmetik hisobni amalga oshirish.

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

Har qanday t sharti uchun t^{1}=t.

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