frac{a^{3}*a^{2}*a^-1}{(a^5/a^8)^-1} eching

$$\frac { a ^ { 3 } \cdot a ^ { 2 } \cdot a ^ { - 1 } } { ( \frac { a ^ { 5 } } { a ^ { 8 } } ) ^ { - 1 } }$$

Baholash

$$a$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 2 ni qo‘shib, 5 ni oling.

$$\frac{a^{5}a^{-1}}{\left(\frac{a^{5}}{a^{8}}\right)^{-1}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 5 va -1 ni qo‘shib, 4 ni oling.

$$\frac{a^{4}}{\left(\frac{a^{5}}{a^{8}}\right)^{-1}}$$

a^{8} ni a^{5}a^{3} sifatida qaytadan yozish. Surat va maxrajdagi ikkala a^{5} ni qisqartiring.

$$\frac{a^{4}}{\left(\frac{1}{a^{3}}\right)^{-1}}$$

\frac{1}{a^{3}}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{a^{4}}{\frac{1^{-1}}{\left(a^{3}\right)^{-1}}}$$

a^{4} ni \frac{1^{-1}}{\left(a^{3}\right)^{-1}} ga bo'lish a^{4} ga k'paytirish \frac{1^{-1}}{\left(a^{3}\right)^{-1}} ga qaytarish.

$$\frac{a^{4}\left(a^{3}\right)^{-1}}{1^{-1}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va -1 ni ko‘paytirib, -3 ni oling.

$$\frac{a^{4}a^{-3}}{1^{-1}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va -3 ni qo‘shib, 1 ni oling.

$$\frac{a^{1}}{1^{-1}}$$

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

$$\frac{a}{1^{-1}}$$

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

$$\frac{a}{1}$$

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$a$$

a ga nisbatan hosilani topish

$$1$$

Derivativ ifodasidan foydalanish qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 2 ni qo‘shib, 5 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{5}a^{-1}}{\left(\frac{a^{5}}{a^{8}}\right)^{-1}})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 5 va -1 ni qo‘shib, 4 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{4}}{\left(\frac{a^{5}}{a^{8}}\right)^{-1}})$$

a^{8} ni a^{5}a^{3} sifatida qaytadan yozish. Surat va maxrajdagi ikkala a^{5} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{4}}{\left(\frac{1}{a^{3}}\right)^{-1}})$$

\frac{1}{a^{3}}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{4}}{\frac{1^{-1}}{\left(a^{3}\right)^{-1}}})$$

a^{4} ni \frac{1^{-1}}{\left(a^{3}\right)^{-1}} ga bo'lish a^{4} ga k'paytirish \frac{1^{-1}}{\left(a^{3}\right)^{-1}} ga qaytarish.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{4}\left(a^{3}\right)^{-1}}{1^{-1}})$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va -1 ni ko‘paytirib, -3 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{4}a^{-3}}{1^{-1}})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va -3 ni qo‘shib, 1 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{1}}{1^{-1}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a}{1^{-1}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a}{1})$$

Har qanday son birga bo‘linganda, natija o‘zi chiqadi.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a)$$

ax^{n} hosilasi – nax^{n-1}.

$$a^{1-1}$$

1 dan 1 ni ayirish.

$$a^{0}$$

Har qanday t sharti uchun (0 bundan mustasno) t^{0}=1.

$$1$$