(x^9)^3/x^6 eching

$$\frac { ( x ^ { 9 } ) ^ { 3 } } { x ^ { 6 } }$$

Baholash

$$x^{21}$$

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\left(x^{9}\right)^{3}\times \frac{1}{x^{6}}$$

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

$$x^{9\times 3}x^{6\left(-1\right)}$$

9 ni 3 marotabaga ko'paytirish.

$$x^{27}x^{6\left(-1\right)}$$

6 ni -1 marotabaga ko'paytirish.

$$x^{27}x^{-6}$$

Ayni daraja ko'rsatkichlarini ko'paytirish uchun ularning darajalarini qo'shing.

$$x^{27-6}$$

27 va -6 belgilarini qo'shish.

$$x^{21}$$

x ga nisbatan hosilani topish

$$21x^{20}$$

Derivativ ifodasidan foydalanish qadamlari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 9 va 3 ni ko‘paytirib, 27 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{27}}{x^{6}})$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun maxrajning darajasini surat darajasidan ayiring. 27 dan 6 ni ayirib, 21 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{21})$$

ax^{n} hosilasi – nax^{n-1}.

$$21x^{21-1}$$

21 dan 1 ni ayirish.

$$21x^{20}$$