g^-1*g^8/g^-57*g^81 eching

$$\frac { g ^ { - 1 } \cdot g ^ { 8 } } { g ^ { - 57 } \cdot g ^ { 81 } }$$

Baholash

$$\frac{1}{g^{17}}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -1 va 8 ni qo‘shib, 7 ni oling.

$$\frac{g^{7}}{g^{-57}g^{81}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -57 va 81 ni qo‘shib, 24 ni oling.

$$\frac{g^{7}}{g^{24}}$$

g^{24} ni g^{7}g^{17} sifatida qaytadan yozish. Surat va maxrajdagi ikkala g^{7} ni qisqartiring.

$$\frac{1}{g^{17}}$$

g ga nisbatan hosilani topish

$$-\frac{17}{g^{18}}$$

Zanjirli qoidadan foydalanish qadamalari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -1 va 8 ni qo‘shib, 7 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{g^{7}}{g^{-57}g^{81}})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -57 va 81 ni qo‘shib, 24 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{g^{7}}{g^{24}})$$

g^{24} ni g^{7}g^{17} sifatida qaytadan yozish. Surat va maxrajdagi ikkala g^{7} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}g}(\frac{1}{g^{17}})$$

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.

$$-\left(g^{17}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}g}(g^{17})$$

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

$$-\left(g^{17}\right)^{-2}\times 17g^{17-1}$$

Qisqartirish.

$$-17g^{16}\left(g^{17}\right)^{-2}$$