(frac{1/2)^{-4}*6^5*2^-2*b}{6^6*2^3} eching

$$\frac { ( \frac { 1 } { 2 } ) ^ { - 4 } \cdot 6 ^ { 5 } \cdot 2 ^ { - 2 } \cdot b } { 6 ^ { 6 } \cdot 2 ^ { 3 } }$$

Baholash

$$\frac{b}{12}$$

Yechim qadamlari

Surat va maxrajdagi ikkala 6^{5} ni qisqartiring.

$$\frac{\left(\frac{1}{2}\right)^{-4}\times 2^{-2}b}{6\times 2^{3}}$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun suratning darajasini maxraj darajasiga bo‘ling.

$$\frac{\left(\frac{1}{2}\right)^{-4}b}{6\times 2^{5}}$$

-4 daraja ko‘rsatkichini \frac{1}{2} ga hisoblang va 16 ni qiymatni oling.

$$\frac{16b}{6\times 2^{5}}$$

5 daraja ko‘rsatkichini 2 ga hisoblang va 32 ni qiymatni oling.

$$\frac{16b}{6\times 32}$$

192 hosil qilish uchun 6 va 32 ni ko'paytirish.

$$\frac{16b}{192}$$

\frac{1}{12}b ni olish uchun 16b ni 192 ga bo‘ling.

$$\frac{1}{12}b$$

b ga nisbatan hosilani topish

$$\frac{1}{12} = 0,08333333333333333$$

Derivativ ifodasidan foydalanish qadamlari

Surat va maxrajdagi ikkala 6^{5} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{\left(\frac{1}{2}\right)^{-4}\times 2^{-2}b}{6\times 2^{3}})$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun suratning darajasini maxraj darajasiga bo‘ling.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{\left(\frac{1}{2}\right)^{-4}b}{6\times 2^{5}})$$

-4 daraja ko‘rsatkichini \frac{1}{2} ga hisoblang va 16 ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{16b}{6\times 2^{5}})$$

5 daraja ko‘rsatkichini 2 ga hisoblang va 32 ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{16b}{6\times 32})$$

192 hosil qilish uchun 6 va 32 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{16b}{192})$$

\frac{1}{12}b ni olish uchun 16b ni 192 ga bo‘ling.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{12}b)$$

ax^{n} hosilasi – nax^{n-1}.

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

1 dan 1 ni ayirish.

$$\frac{1}{12}b^{0}$$

Har qanday t sharti uchun (0 bundan mustasno) t^{0}=1.

$$\frac{1}{12}\times 1$$

Har qanday t sharti uchun t\times 1=t va 1t=t.

$$\frac{1}{12}$$