frac{3x^{6}y^4z^-5}{15x^-2y^-7} eching

$$\frac { 3 x ^ { 6 } y ^ { 4 } z ^ { - 5 } } { 15 x ^ { - 2 } y ^ { - 7 } }$$

Baholash

$$\frac{x^{8}y^{11}}{5z^{5}}$$

Yechim qadamlari

Surat va maxrajdagi ikkala 3 ni qisqartiring.

$$\frac{z^{-5}y^{4}x^{6}}{5y^{-7}x^{-2}}$$

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

$$\frac{z^{-5}x^{8}y^{11}}{5}$$

x ga nisbatan hosilani topish

$$\frac{8x^{7}y^{11}}{5z^{5}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3y^{4}}{z^{5}\times \frac{15}{y^{7}}}x^{6-\left(-2\right)})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{y^{11}}{5z^{5}}x^{8})$$

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

$$8\times \frac{y^{11}}{5z^{5}}x^{8-1}$$

Arifmetik hisobni amalga oshirish.

$$\frac{8y^{11}}{5z^{5}}x^{7}$$