15n^53n^545n^2 eching

$$15 n ^ { 5 } 3 n ^ { 5 } 45 n ^ { 2 }$$

Baholash

$$2025n^{12}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 5 va 5 ni qo‘shib, 10 ni oling.

$$15n^{10}\times 3\times 45n^{2}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 10 va 2 ni qo‘shib, 12 ni oling.

$$15n^{12}\times 3\times 45$$

45 hosil qilish uchun 15 va 3 ni ko'paytirish.

$$45n^{12}\times 45$$

2025 hosil qilish uchun 45 va 45 ni ko'paytirish.

$$2025n^{12}$$

n ga nisbatan hosilani topish

$$24300n^{11}$$

Derivativ ifodasidan foydalanish qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 5 va 5 ni qo‘shib, 10 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}n}(15n^{10}\times 3\times 45n^{2})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 10 va 2 ni qo‘shib, 12 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}n}(15n^{12}\times 3\times 45)$$

45 hosil qilish uchun 15 va 3 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}n}(45n^{12}\times 45)$$

2025 hosil qilish uchun 45 va 45 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}n}(2025n^{12})$$

ax^{n} hosilasi – nax^{n-1}.

$$12\times 2025n^{12-1}$$

12 ni 2025 marotabaga ko'paytirish.

$$24300n^{12-1}$$

12 dan 1 ni ayirish.

$$24300n^{11}$$