(a^-7diva^15)div(a^-6)^4/a eching

$$\frac { ( a ^ { - 7 } \div a ^ { 15 } ) \div ( a ^ { - 6 } ) ^ { 4 } } { a }$$

Baholash

$$a$$

Yechim qadamlari

a^{15} ni a^{-7}a^{22} sifatida qaytadan yozish. Surat va maxrajdagi ikkala a^{-7} ni qisqartiring.

$$\frac{\frac{\frac{1}{a^{22}}}{\left(a^{-6}\right)^{4}}}{a}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -6 va 4 ni ko‘paytirib, -24 ni oling.

$$\frac{\frac{\frac{1}{a^{22}}}{a^{-24}}}{a}$$

\frac{\frac{\frac{1}{a^{22}}}{a^{-24}}}{a} ni yagona kasrga aylantiring.

$$\frac{\frac{1}{a^{22}}}{a^{-24}a}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -24 va 1 ni qo‘shib, -23 ni oling.

$$\frac{\frac{1}{a^{22}}}{a^{-23}}$$

\frac{\frac{1}{a^{22}}}{a^{-23}} ni yagona kasrga aylantiring.

$$\frac{1}{a^{22}a^{-23}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 22 va -23 ni qo‘shib, -1 ni oling.

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

a ga nisbatan hosilani topish

$$1$$

Zanjirli qoidadan foydalanish qadamalari

a^{15} ni a^{-7}a^{22} sifatida qaytadan yozish. Surat va maxrajdagi ikkala a^{-7} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{\frac{1}{a^{22}}}{\left(a^{-6}\right)^{4}}}{a})$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. -6 va 4 ni ko‘paytirib, -24 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{\frac{1}{a^{22}}}{a^{-24}}}{a})$$

\frac{\frac{\frac{1}{a^{22}}}{a^{-24}}}{a} ni yagona kasrga aylantiring.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{1}{a^{22}}}{a^{-24}a})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -24 va 1 ni qo‘shib, -23 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{1}{a^{22}}}{a^{-23}})$$

\frac{\frac{1}{a^{22}}}{a^{-23}} ni yagona kasrga aylantiring.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{a^{22}a^{-23}})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 22 va -23 ni qo‘shib, -1 ni oling.

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

Agar F ikki differensial funksiya f\left(u\right) va u=g\left(x\right)'ning yig'indisi bo'lsa, ya'ni agar F\left(x\right)=f\left(g\left(x\right)\right) bo'lsa, F hosilasi f'ning u martalik hosilasi, g'ning x martalik hosilasi ya'ni \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right) bo'ladi.

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

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

$$-\left(\frac{1}{a}\right)^{-2}\left(-1\right)a^{-1-1}$$

Qisqartirish.

$$a^{-2}\times \left(\frac{1}{a}\right)^{-2}$$