(x^4)^4/x^6 eching

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

Baholash

$$x^{10}$$

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

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

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

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

4 ni 4 marotabaga ko'paytirish.

$$x^{16}x^{6\left(-1\right)}$$

6 ni -1 marotabaga ko'paytirish.

$$x^{16}x^{-6}$$

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

$$x^{16-6}$$

16 va -6 belgilarini qo'shish.

$$x^{10}$$

x ga nisbatan hosilani topish

$$10x^{9}$$

Derivativ ifodasidan foydalanish qadamlari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 4 va 4 ni ko‘paytirib, 16 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{16}}{x^{6}})$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun maxrajning darajasini surat darajasidan ayiring. 16 dan 6 ni ayirib, 10 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{10})$$

ax^{n} hosilasi – nax^{n-1}.

$$10x^{10-1}$$

10 dan 1 ni ayirish.

$$10x^{9}$$