r^-5*r^-1/r^8*r^-5 eching

$$\frac { r ^ { - 5 } \cdot r ^ { - 1 } } { r ^ { 8 } \cdot r ^ { - 5 } }$$

Baholash

$$\frac{1}{r^{9}}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -5 va -1 ni qo‘shib, -6 ni oling.

$$\frac{r^{-6}}{r^{8}r^{-5}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 8 va -5 ni qo‘shib, 3 ni oling.

$$\frac{r^{-6}}{r^{3}}$$

r^{3} ni r^{-6}r^{9} sifatida qaytadan yozish. Surat va maxrajdagi ikkala r^{-6} ni qisqartiring.

$$\frac{1}{r^{9}}$$

r ga nisbatan hosilani topish

$$-\frac{9}{r^{10}}$$

Zanjirli qoidadan foydalanish qadamalari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. -5 va -1 ni qo‘shib, -6 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{r^{-6}}{r^{8}r^{-5}})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 8 va -5 ni qo‘shib, 3 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{r^{-6}}{r^{3}})$$

r^{3} ni r^{-6}r^{9} sifatida qaytadan yozish. Surat va maxrajdagi ikkala r^{-6} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{1}{r^{9}})$$

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.

$$-\left(r^{9}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}r}(r^{9})$$

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

$$-\left(r^{9}\right)^{-2}\times 9r^{9-1}$$

Qisqartirish.

$$-9r^{8}\left(r^{9}\right)^{-2}$$