(64x^9)^1/3 eching

$$( 64 x ^ { 9 } ) ^ { 1 / 3 }$$

Baholash

$$4x^{3}$$

Oshib boruvchi tartibdan boshqa tartib uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\sqrt[3]{64x^{9}}$$

Ikki yoki undan ko'p raqam koʻpaytmasini daraja ko'rsatkichiga oshirish uchun har bir raqamni daraja ko'rsatkichiga oshiring va ularning koʻpaytmasini chiqaring.

$$\sqrt[3]{64}\sqrt[3]{x^{9}}$$

64 ni \frac{1}{3} daraja ko'rsatgichiga oshirish.

$$4\sqrt[3]{x^{9}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring.

$$4x^{9\times \frac{1}{3}}$$

9 ni \frac{1}{3} marotabaga ko'paytirish.

$$4x^{3}$$

x ga nisbatan hosilani topish

$$12x^{2}$$

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.

$$\frac{1}{3}\times \left(64x^{9}\right)^{\frac{1}{3}-1}\frac{\mathrm{d}}{\mathrm{d}x}(64x^{9})$$

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

$$\frac{1}{3}\times \left(64x^{9}\right)^{-\frac{2}{3}}\times 9\times 64x^{9-1}$$

Qisqartirish.

$$192x^{8}\times \left(64x^{9}\right)^{-\frac{2}{3}}$$