(z^2)^2/(z^6)^8= eching

$$\frac { ( z ^ { 2 } ) ^ { 2 } } { ( z ^ { 6 } ) ^ { 8 } } =$$

Baholash

$$\frac{1}{z^{44}}$$

Yechim qadamlari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 2 ni ko‘paytirib, 4 ni oling.

$$\frac{z^{4}}{\left(z^{6}\right)^{8}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 6 va 8 ni ko‘paytirib, 48 ni oling.

$$\frac{z^{4}}{z^{48}}$$

z^{48} ni z^{4}z^{44} sifatida qaytadan yozish. Surat va maxrajdagi ikkala z^{4} ni qisqartiring.

$$\frac{1}{z^{44}}$$

z ga nisbatan hosilani topish

$$-\frac{44}{z^{45}}$$

Zanjirli qoidadan foydalanish qadamalari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 2 ni ko‘paytirib, 4 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{z^{4}}{\left(z^{6}\right)^{8}})$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 6 va 8 ni ko‘paytirib, 48 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{z^{4}}{z^{48}})$$

z^{48} ni z^{4}z^{44} sifatida qaytadan yozish. Surat va maxrajdagi ikkala z^{4} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{1}{z^{44}})$$

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.

$$-\left(z^{44}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}z}(z^{44})$$

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

$$-\left(z^{44}\right)^{-2}\times 44z^{44-1}$$

Qisqartirish.

$$-44z^{43}\left(z^{44}\right)^{-2}$$