frac{25x^{-8}y^9(x)^-2}{5x^-8y^-9} eching

$$\frac { 25 x ^ { - 8 } y ^ { 9 } ( x ) ^ { - 2 } } { 5 x ^ { - 8 } y ^ { - 9 } }$$

Baholash

$$\frac{5y^{18}}{x^{2}}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -8 va -2 ni qo‘shib, -10 ni oling.

$$\frac{25x^{-10}y^{9}}{5x^{-8}y^{-9}}$$

Surat va maxrajdagi ikkala 5 ni qisqartiring.

$$\frac{5x^{-10}y^{9}}{y^{-9}x^{-8}}$$

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

$$\frac{5x^{-10}y^{18}}{x^{-8}}$$

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

$$\frac{5y^{18}}{x^{2}}$$

x ga nisbatan hosilani topish

$$-\frac{10y^{18}}{x^{3}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{25y^{9}}{x^{2}\times \frac{5}{y^{9}}}x^{-8-\left(-8\right)})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5y^{18}}{x^{2}}x^{0})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5y^{18}}{x^{2}})$$

Konstantaning hosilasi 0 ga teng.

$$0$$