2x^2y^2/4x^2y^43{x^-3} eching

$$\frac{ 2 { x }^{ 2 } { y }^{ 2 } }{ 4 { x }^{ 2 } { y }^{ 4 } 3 { x }^{ -3 } }$$

Baholash

$$\frac{x^{3}}{6y^{2}}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va -3 ni qo‘shib, -1 ni oling.

$$\frac{2x^{2}y^{2}}{4x^{-1}y^{4}\times 3}$$

Surat va maxrajdagi ikkala 2y^{2} ni qisqartiring.

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

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

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

6 hosil qilish uchun 2 va 3 ni ko'paytirish.

$$\frac{x^{3}}{6y^{2}}$$

x ga nisbatan hosilani topish

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

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2y^{2}x^{3}}{12y^{4}}x^{2-2})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{3}}{6y^{2}}x^{0})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{3}}{6y^{2}})$$

Konstantaning hosilasi 0 ga teng.

$$0$$