6x^frac{2{3}}*3x*x^-3 eching

$$6 x ^ { \frac { 2 } { 3 } } \cdot 3 x \cdot x ^ { - 3 }$$

Baholash

$$\frac{18}{x^{\frac{4}{3}}}$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{2}{3} va 1 ni qo‘shib, \frac{5}{3} ni oling.

$$6x^{\frac{5}{3}}\times 3x^{-3}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{5}{3} va -3 ni qo‘shib, -\frac{4}{3} ni oling.

$$6x^{-\frac{4}{3}}\times 3$$

18 hosil qilish uchun 6 va 3 ni ko'paytirish.

$$18x^{-\frac{4}{3}}$$

x ga nisbatan hosilani topish

$$-\frac{24}{x^{\frac{7}{3}}}$$

Derivativ ifodasidan foydalanish qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{2}{3} va 1 ni qo‘shib, \frac{5}{3} ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{\frac{5}{3}}\times 3x^{-3})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{5}{3} va -3 ni qo‘shib, -\frac{4}{3} ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{-\frac{4}{3}}\times 3)$$

18 hosil qilish uchun 6 va 3 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(18x^{-\frac{4}{3}})$$

ax^{n} hosilasi – nax^{n-1}.

$$-\frac{4}{3}\times 18x^{-\frac{4}{3}-1}$$

-\frac{4}{3} ni 18 marotabaga ko'paytirish.

$$-24x^{-\frac{4}{3}-1}$$

-\frac{4}{3} dan 1 ni ayirish.

$$-24x^{-\frac{7}{3}}$$