frac{2^{-2}x^{2}y^-4}{5^-2x^7y^-1} eching

$$\frac { 2 ^ { - 2 } x ^ { 2 } y ^ { - 4 } } { 5 ^ { - 2 } x ^ { 7 } y ^ { - 1 } }$$

Baholash

$$\frac{25}{4y^{3}x^{5}}$$

Yechim qadamlari

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

$$\frac{2^{-2}y^{-4}}{5^{-2}\times \frac{1}{y}x^{5}}$$

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

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

-2 daraja ko‘rsatkichini 2 ga hisoblang va \frac{1}{4} ni qiymatni oling.

$$\frac{\frac{1}{4}}{5^{-2}y^{3}x^{5}}$$

-2 daraja ko‘rsatkichini 5 ga hisoblang va \frac{1}{25} ni qiymatni oling.

$$\frac{\frac{1}{4}}{\frac{1}{25}y^{3}x^{5}}$$

\frac{\frac{1}{4}}{\frac{1}{25}y^{3}x^{5}} ni yagona kasrga aylantiring.

$$\frac{1}{4\times \frac{1}{25}y^{3}x^{5}}$$

\frac{4}{25} hosil qilish uchun 4 va \frac{1}{25} ni ko'paytirish.

$$\frac{1}{\frac{4}{25}y^{3}x^{5}}$$

x ga nisbatan hosilani topish

$$-\frac{125}{4y^{3}x^{6}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{4y^{4}\times \frac{1}{25y}}x^{2-7})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{25}{4y^{3}}x^{-5})$$

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

$$-5\times \frac{25}{4y^{3}}x^{-5-1}$$

Arifmetik hisobni amalga oshirish.

$$\left(-\frac{125}{4y^{3}}\right)x^{-6}$$