(4b)^1/2(8b^1/4) eching

$$( 4 b ) ^ { 1 / 2 } ( 8 b ^ { 1 / 4 } )$$

Baholash

$$16b^{\frac{3}{4}}$$

Yechim qadamlari

\left(4b\right)^{\frac{1}{2}} ni kengaytirish.

$$4^{\frac{1}{2}}b^{\frac{1}{2}}\times 8b^{\frac{1}{4}}$$

\frac{1}{2} daraja ko‘rsatkichini 4 ga hisoblang va 2 ni qiymatni oling.

$$2b^{\frac{1}{2}}\times 8b^{\frac{1}{4}}$$

16 hosil qilish uchun 2 va 8 ni ko'paytirish.

$$16b^{\frac{1}{2}}b^{\frac{1}{4}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{1}{2} va \frac{1}{4} ni qo‘shib, \frac{3}{4} ni oling.

$$16b^{\frac{3}{4}}$$

b ga nisbatan hosilani topish

$$\frac{12}{\sqrt[4]{b}}$$

Derivativ ifodasidan foydalanish qadamlari

\left(4b\right)^{\frac{1}{2}} ni kengaytirish.

$$\frac{\mathrm{d}}{\mathrm{d}b}(4^{\frac{1}{2}}b^{\frac{1}{2}}\times 8b^{\frac{1}{4}})$$

\frac{1}{2} daraja ko‘rsatkichini 4 ga hisoblang va 2 ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}b}(2b^{\frac{1}{2}}\times 8b^{\frac{1}{4}})$$

16 hosil qilish uchun 2 va 8 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}b}(16b^{\frac{1}{2}}b^{\frac{1}{4}})$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. \frac{1}{2} va \frac{1}{4} ni qo‘shib, \frac{3}{4} ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}b}(16b^{\frac{3}{4}})$$

ax^{n} hosilasi – nax^{n-1}.

$$\frac{3}{4}\times 16b^{\frac{3}{4}-1}$$

\frac{3}{4} ni 16 marotabaga ko'paytirish.

$$12b^{\frac{3}{4}-1}$$

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

$$12b^{-\frac{1}{4}}$$