yfrac{(-2)^{10}*5^{6}*6^3}{(-2)^6*5^3*6^2} eching

$$y \frac { ( - 2 ) ^ { 10 } \cdot 5 ^ { 6 } \cdot 6 ^ { 3 } } { ( - 2 ) ^ { 6 } \cdot 5 ^ { 3 } \cdot 6 ^ { 2 } }$$

Baholash

$$12000y$$

Yechim qadamlari

Surat va maxrajdagi ikkala \left(-2\right)^{6}\times 5^{3}\times 6^{2} ni qisqartiring.

$$y\times 6\left(-2\right)^{4}\times 5^{3}$$

4 daraja ko‘rsatkichini -2 ga hisoblang va 16 ni qiymatni oling.

$$y\times 6\times 16\times 5^{3}$$

96 hosil qilish uchun 6 va 16 ni ko'paytirish.

$$y\times 96\times 5^{3}$$

3 daraja ko‘rsatkichini 5 ga hisoblang va 125 ni qiymatni oling.

$$y\times 96\times 125$$

12000 hosil qilish uchun 96 va 125 ni ko'paytirish.

$$y\times 12000$$

y ga nisbatan hosilani topish

$$12000$$

Derivativ ifodasidan foydalanish qadamlari

Surat va maxrajdagi ikkala \left(-2\right)^{6}\times 5^{3}\times 6^{2} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y\times 6\left(-2\right)^{4}\times 5^{3})$$

4 daraja ko‘rsatkichini -2 ga hisoblang va 16 ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y\times 6\times 16\times 5^{3})$$

96 hosil qilish uchun 6 va 16 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y\times 96\times 5^{3})$$

3 daraja ko‘rsatkichini 5 ga hisoblang va 125 ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y\times 96\times 125)$$

12000 hosil qilish uchun 96 va 125 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}y}(y\times 12000)$$

ax^{n} hosilasi – nax^{n-1}.

$$12000y^{1-1}$$

1 dan 1 ni ayirish.

$$12000y^{0}$$

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

$$12000\times 1$$

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

$$12000$$