{left(sqrt{x^4}right)}^2*{left(sqrt{x^8}right)}^2*{left(sqrt{x^2}right)}^2 eching

$${ \left( \sqrt{ { x }^{ 4 } } \right) }^{ 2 } \times { \left( \sqrt{ { x }^{ 8 } } \right) }^{ 2 } \times { \left( \sqrt{ { x }^{ 2 } } \right) }^{ 2 }$$

Baholash

$$x^{14}$$

Yechim qadamlari

2 daraja ko‘rsatkichini \sqrt{x^{4}} ga hisoblang va x^{4} ni qiymatni oling.

$$x^{4}\left(\sqrt{x^{8}}\right)^{2}\left(\sqrt{x^{2}}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{x^{8}} ga hisoblang va x^{8} ni qiymatni oling.

$$x^{4}x^{8}\left(\sqrt{x^{2}}\right)^{2}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va 8 ni qo‘shib, 12 ni oling.

$$x^{12}\left(\sqrt{x^{2}}\right)^{2}$$

2 daraja ko‘rsatkichini \sqrt{x^{2}} ga hisoblang va x^{2} ni qiymatni oling.

$$x^{12}x^{2}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 12 va 2 ni qo‘shib, 14 ni oling.

$$x^{14}$$

x ga nisbatan hosilani topish

$$14x^{13}$$

Derivativ ifodasidan foydalanish qadamlari

2 daraja ko‘rsatkichini \sqrt{x^{4}} ga hisoblang va x^{4} ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}\left(\sqrt{x^{8}}\right)^{2}\left(\sqrt{x^{2}}\right)^{2})$$

2 daraja ko‘rsatkichini \sqrt{x^{8}} ga hisoblang va x^{8} ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}x^{8}\left(\sqrt{x^{2}}\right)^{2})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va 8 ni qo‘shib, 12 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{12}\left(\sqrt{x^{2}}\right)^{2})$$

2 daraja ko‘rsatkichini \sqrt{x^{2}} ga hisoblang va x^{2} ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{12}x^{2})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 12 va 2 ni qo‘shib, 14 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{14})$$

ax^{n} hosilasi – nax^{n-1}.

$$14x^{14-1}$$

14 dan 1 ni ayirish.

$$14x^{13}$$