n^8/(n^6)^4 eching

$$\frac { n ^ { 8 } } { ( n ^ { 6 } ) ^ { 4 } }$$

Baholash

$$\frac{1}{n^{16}}$$

Yechim qadamlari

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

$$\frac{n^{8}}{n^{24}}$$

n^{24} ni n^{8}n^{16} sifatida qaytadan yozish. Surat va maxrajdagi ikkala n^{8} ni qisqartiring.

$$\frac{1}{n^{16}}$$

n ga nisbatan hosilani topish

$$-\frac{16}{n^{17}}$$

Zanjirli qoidadan foydalanish qadamalari

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{n^{8}}{n^{24}})$$

n^{24} ni n^{8}n^{16} sifatida qaytadan yozish. Surat va maxrajdagi ikkala n^{8} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{1}{n^{16}})$$

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.

$$-\left(n^{16}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}n}(n^{16})$$

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

$$-\left(n^{16}\right)^{-2}\times 16n^{16-1}$$

Qisqartirish.

$$-16n^{15}\left(n^{16}\right)^{-2}$$