frac{10^{5}x6^5x24}{48^2x15^4x4^3} eching

$$\frac { 10 ^ { 5 } x 6 ^ { 5 } x 24 } { 48 ^ { 2 } x 15 ^ { 4 } x 4 ^ { 3 } }$$

Baholash

$$\frac{5x_{24}}{48x}$$

Yechim qadamlari

x^{2} hosil qilish uchun x va x ni ko'paytirish.

$$\frac{10^{5}x\times 6^{5}x_{24}}{48^{2}x^{2}\times 15^{4}\times 4^{3}}$$

Surat va maxrajdagi ikkala x ni qisqartiring.

$$\frac{6^{5}\times 10^{5}x_{24}}{4^{3}\times 15^{4}\times 48^{2}x}$$

5 daraja ko‘rsatkichini 6 ga hisoblang va 7776 ni qiymatni oling.

$$\frac{7776\times 10^{5}x_{24}}{4^{3}\times 15^{4}\times 48^{2}x}$$

5 daraja ko‘rsatkichini 10 ga hisoblang va 100000 ni qiymatni oling.

$$\frac{7776\times 100000x_{24}}{4^{3}\times 15^{4}\times 48^{2}x}$$

777600000 hosil qilish uchun 7776 va 100000 ni ko'paytirish.

$$\frac{777600000x_{24}}{4^{3}\times 15^{4}\times 48^{2}x}$$

3 daraja ko‘rsatkichini 4 ga hisoblang va 64 ni qiymatni oling.

$$\frac{777600000x_{24}}{64\times 15^{4}\times 48^{2}x}$$

4 daraja ko‘rsatkichini 15 ga hisoblang va 50625 ni qiymatni oling.

$$\frac{777600000x_{24}}{64\times 50625\times 48^{2}x}$$

3240000 hosil qilish uchun 64 va 50625 ni ko'paytirish.

$$\frac{777600000x_{24}}{3240000\times 48^{2}x}$$

2 daraja ko‘rsatkichini 48 ga hisoblang va 2304 ni qiymatni oling.

$$\frac{777600000x_{24}}{3240000\times 2304x}$$

7464960000 hosil qilish uchun 3240000 va 2304 ni ko'paytirish.

$$\frac{777600000x_{24}}{7464960000x}$$

Surat va maxrajdagi ikkala 155520000 ni qisqartiring.

$$\frac{5x_{24}}{48x}$$

x ga nisbatan hosilani topish

$$-\frac{5x_{24}}{48x^{2}}$$

Yechim qadamlari

Ayni asosning daraja ko'rsatkichi bo'lish uchun maxrajning darajasini surat darajasidan bo'ling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{777600000x_{24}}{7464960000x}x^{1-1})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x_{24}}{48x}x^{0})$$

Har qanday a raqami uchun (0 bundan mustasno) a^{0}=1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x_{24}}{48x})$$

Konstantaning hosilasi 0 ga teng.

$$0$$