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

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

Baholash

$$\frac{1}{a^{46}}$$

Yechim qadamlari

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

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

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

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

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

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

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 22 va 24 ni qo‘shib, 46 ni oling.

$$\frac{1}{a^{46}}$$

a ga nisbatan hosilani topish

$$-\frac{46}{a^{47}}$$

Zanjirli qoidadan foydalanish qadamalari

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

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

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

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

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

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

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 22 va 24 ni qo‘shib, 46 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{a^{46}})$$

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.

$$-\left(a^{46}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}a}(a^{46})$$

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

$$-\left(a^{46}\right)^{-2}\times 46a^{46-1}$$

Qisqartirish.

$$-46a^{45}\left(a^{46}\right)^{-2}$$