frac{(12x^{3}y^{2})*(3x^{5}yz^6)}{9x^-4y^3z^3}= eching

$$\frac { ( 12 x ^ { 3 } y ^ { 2 } ) \times ( 3 x ^ { 5 } y z ^ { 6 } ) } { 9 x ^ { - 4 } y ^ { 3 } z ^ { 3 } } =$$

Baholash

$$4z^{3}x^{12}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 5 ni qo‘shib, 8 ni oling.

$$\frac{12x^{8}y^{2}\times 3yz^{6}}{9x^{-4}y^{3}z^{3}}$$

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

$$\frac{12x^{8}y^{3}\times 3z^{6}}{9x^{-4}y^{3}z^{3}}$$

Surat va maxrajdagi ikkala 3\times 3y^{3}z^{3} ni qisqartiring.

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

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

$$4z^{3}x^{12}$$

x ga nisbatan hosilani topish

$$48z^{3}x^{11}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{36y^{3}x^{5}z^{6}}{9y^{3}z^{3}}x^{3-\left(-4\right)})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4z^{3}x^{5}x^{7})$$

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

$$7\times 4z^{3}x^{5}x^{7-1}$$

Arifmetik hisobni amalga oshirish.

$$28z^{3}x^{5}x^{6}$$