(u^2)^6(u^5)^6 eching

$$( u ^ { 2 } ) ^ { 6 } ( u ^ { 5 } ) ^ { 6 }$$

Baholash

$$u^{42}$$

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

$$\left(u^{2}\right)^{6}\left(u^{5}\right)^{6}$$

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

$$u^{2\times 6}u^{5\times 6}$$

2 ni 6 marotabaga ko'paytirish.

$$u^{12}u^{5\times 6}$$

5 ni 6 marotabaga ko'paytirish.

$$u^{12}u^{30}$$

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

$$u^{12+30}$$

12 va 30 belgilarini qo'shish.

$$u^{42}$$

u ga nisbatan hosilani topish

$$42u^{41}$$

Derivativ ifodasidan foydalanish qadamlari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va 6 ni ko‘paytirib, 12 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{12}\left(u^{5}\right)^{6})$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 5 va 6 ni ko‘paytirib, 30 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{12}u^{30})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 12 va 30 ni qo‘shib, 42 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{42})$$

ax^{n} hosilasi – nax^{n-1}.

$$42u^{42-1}$$

42 dan 1 ni ayirish.

$$42u^{41}$$