(64x^4)^frac{5{6}} eching

$$( 64 x ^ { 4 } ) ^ { \frac { 5 } { 6 } }$$

Baholash

$$32x^{\frac{10}{3}}$$

Yechim qadamlari

\left(64x^{4}\right)^{\frac{5}{6}} ni kengaytirish.

$$64^{\frac{5}{6}}\left(x^{4}\right)^{\frac{5}{6}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 4 va \frac{5}{6} ni ko‘paytirib, \frac{10}{3} ni oling.

$$64^{\frac{5}{6}}x^{\frac{10}{3}}$$

\frac{5}{6} daraja ko‘rsatkichini 64 ga hisoblang va 32 ni qiymatni oling.

$$32x^{\frac{10}{3}}$$

x ga nisbatan hosilani topish

$$\frac{320x^{\frac{7}{3}}}{3}$$

Zanjirli qoidadan foydalanish qadamalari

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.

$$\frac{5}{6}\times \left(64x^{4}\right)^{\frac{5}{6}-1}\frac{\mathrm{d}}{\mathrm{d}x}(64x^{4})$$

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

$$\frac{5}{6}\times \left(64x^{4}\right)^{-\frac{1}{6}}\times 4\times 64x^{4-1}$$

Qisqartirish.

$$\frac{640}{3}x^{3}\times \left(64x^{4}\right)^{-\frac{1}{6}}$$