frac{3x^{2}y^{-3}z^{4}}{yx^2z^3*2xy^4z^-3} eching

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

Baholash

$$\frac{3z^{4}}{2xy^{8}}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 4 ni qo‘shib, 5 ni oling.

$$\frac{3x^{2}y^{-3}z^{4}}{y^{5}x^{2}z^{3}\times 2xz^{-3}}$$

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

$$\frac{3x^{2}y^{-3}z^{4}}{y^{5}x^{3}z^{3}\times 2z^{-3}}$$

1 hosil qilish uchun z^{3} va z^{-3} ni ko'paytirish.

$$\frac{3x^{2}y^{-3}z^{4}}{y^{5}x^{3}\times 2}$$

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

$$\frac{3y^{-3}z^{4}}{2xy^{5}}$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun suratning darajasini maxraj darajasiga bo‘ling.

$$\frac{3z^{4}}{2xy^{8}}$$

x ga nisbatan hosilani topish

$$-\frac{3z^{4}}{2x^{2}y^{8}}$$

Yechim qadamlari

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

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

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3z^{4}}{2xy^{8}}x^{0})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3z^{4}}{2xy^{8}})$$

Konstantaning hosilasi 0 ga teng.

$$0$$