{left(x^3right)}^frac{1{3}}*{left(x^4right)}^frac{1{2}}*{left(x1/5right)}^5 eching

$${ \left( { x }^{ 3 } \right) }^{ \frac{ 1 }{ 3 } } \times { \left( { x }^{ 4 } \right) }^{ \frac{ 1 }{ 2 } } \times { \left(x \frac{ 1 }{ 5 } \right) }^{ 5 }$$

Baholash

$$\frac{x^{8}}{3125}$$

Yechim qadamlari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va \frac{1}{3} ni ko‘paytirib, 1 ni oling.

$$x^{1}\left(x^{4}\right)^{\frac{1}{2}}\left(x\times \frac{1}{5}\right)^{5}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 4 va \frac{1}{2} ni ko‘paytirib, 2 ni oling.

$$x^{1}x^{2}\left(x\times \frac{1}{5}\right)^{5}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 2 ni qo‘shib, 3 ni oling.

$$x^{3}\left(x\times \frac{1}{5}\right)^{5}$$

\left(x\times \frac{1}{5}\right)^{5} ni kengaytirish.

$$x^{3}x^{5}\times \left(\frac{1}{5}\right)^{5}$$

5 daraja ko‘rsatkichini \frac{1}{5} ga hisoblang va \frac{1}{3125} ni qiymatni oling.

$$x^{3}x^{5}\times \frac{1}{3125}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 5 ni qo‘shib, 8 ni oling.

$$x^{8}\times \frac{1}{3125}$$

x ga nisbatan hosilani topish

$$\frac{8x^{7}}{3125}$$

Derivativ ifodasidan foydalanish qadamlari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va \frac{1}{3} ni ko‘paytirib, 1 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}\left(x^{4}\right)^{\frac{1}{2}}\left(x\times \frac{1}{5}\right)^{5})$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 4 va \frac{1}{2} ni ko‘paytirib, 2 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}x^{2}\left(x\times \frac{1}{5}\right)^{5})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 1 va 2 ni qo‘shib, 3 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\left(x\times \frac{1}{5}\right)^{5})$$

\left(x\times \frac{1}{5}\right)^{5} ni kengaytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}x^{5}\times \left(\frac{1}{5}\right)^{5})$$

5 daraja ko‘rsatkichini \frac{1}{5} ga hisoblang va \frac{1}{3125} ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}x^{5}\times \frac{1}{3125})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 5 ni qo‘shib, 8 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{8}\times \frac{1}{3125})$$

ax^{n} hosilasi – nax^{n-1}.

$$8\times \frac{1}{3125}x^{8-1}$$

8 ni \frac{1}{3125} marotabaga ko'paytirish.

$$\frac{8}{3125}x^{8-1}$$

8 dan 1 ni ayirish.

$$\frac{8}{3125}x^{7}$$