5a^-7b^4/20a^3b^-2 eching

$$\frac { 5 a ^ { - 7 } b ^ { 4 } } { 20 a ^ { 3 } b ^ { - 2 } }$$

Baholash

$$\frac{b^{6}}{4a^{10}}$$

Yechim qadamlari

Surat va maxrajdagi ikkala 5 ni qisqartiring.

$$\frac{a^{-7}b^{4}}{4b^{-2}a^{3}}$$

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

$$\frac{a^{-7}b^{6}}{4a^{3}}$$

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

$$\frac{b^{6}}{4a^{10}}$$

a ga nisbatan hosilani topish

$$-\frac{5b^{6}}{2a^{11}}$$

Yechim qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{5b^{4}b^{2}}{20}a^{-7-3})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{b^{6}}{4}a^{-10})$$

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

$$-10\times \frac{b^{6}}{4}a^{-10-1}$$

Arifmetik hisobni amalga oshirish.

$$\left(-\frac{5b^{6}}{2}\right)a^{-11}$$