4x^4x^-8/8x^-7y^-2 eching

$$\frac { 4 x ^ { 4 } x ^ { - 8 } } { 8 x ^ { - 7 } y ^ { - 2 } }$$

Baholash

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

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va -8 ni qo‘shib, -4 ni oling.

$$\frac{4x^{-4}}{8x^{-7}y^{-2}}$$

Surat va maxrajdagi ikkala 4 ni qisqartiring.

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

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

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

x ga nisbatan hosilani topish

$$\frac{3\left(xy\right)^{2}}{2}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{x^{8}\times \frac{8}{y^{2}}}x^{4-\left(-7\right)})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{y^{2}}{2x^{8}}x^{11})$$

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

$$11\times \frac{y^{2}}{2x^{8}}x^{11-1}$$

Arifmetik hisobni amalga oshirish.

$$\frac{11y^{2}}{2x^{8}}x^{10}$$