frac{24x^{-3}y^{4}z^2}{36x^-2y^-7z^5} eching

$$\frac { 24 x ^ { - 3 } y ^ { 4 } z ^ { 2 } } { 36 x ^ { - 2 } y ^ { - 7 } z ^ { 5 } }$$

Baholash

$$\frac{2y^{11}}{3xz^{3}}$$

Yechim qadamlari

Surat va maxrajdagi ikkala 12z^{2} ni qisqartiring.

$$\frac{2x^{-3}y^{4}}{3y^{-7}x^{-2}z^{3}}$$

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

$$\frac{2x^{-3}y^{11}}{3x^{-2}z^{3}}$$

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

$$\frac{2y^{11}}{3x^{1}z^{3}}$$

1 daraja ko‘rsatkichini x ga hisoblang va x ni qiymatni oling.

$$\frac{2y^{11}}{3xz^{3}}$$

x ga nisbatan hosilani topish

$$-\frac{2y^{11}}{3x^{2}z^{3}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24z^{2}y^{4}y^{7}}{36z^{5}}x^{-3-\left(-2\right)})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2y^{11}}{3z^{3}}\times \frac{1}{x})$$

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

$$-\frac{2y^{11}}{3z^{3}}x^{-1-1}$$

Arifmetik hisobni amalga oshirish.

$$\left(-\frac{2y^{11}}{3z^{3}}\right)x^{-2}$$