5x^3*4x:10x^2-16x^3:4x^2*2x eching

$$5 x ^ { 3 } \cdot 4 x : 10 x ^ { 2 } - 16 x ^ { 3 } : 4 x ^ { 2 } \cdot 2 x$$

Baholash

$$-6x^{6}$$

Yechim qadamlari

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

$$\frac{5x^{4}\times 4}{10}x^{2}-\frac{16x^{3}}{4}x^{2}\times 2x$$

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

$$\frac{5x^{4}\times 4}{10}x^{2}-\frac{16x^{3}}{4}x^{3}\times 2$$

20 hosil qilish uchun 5 va 4 ni ko'paytirish.

$$\frac{20x^{4}}{10}x^{2}-\frac{16x^{3}}{4}x^{3}\times 2$$

2x^{4} ni olish uchun 20x^{4} ni 10 ga bo‘ling.

$$2x^{4}x^{2}-\frac{16x^{3}}{4}x^{3}\times 2$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va 2 ni qo‘shib, 6 ni oling.

$$2x^{6}-\frac{16x^{3}}{4}x^{3}\times 2$$

4x^{3} ni olish uchun 16x^{3} ni 4 ga bo‘ling.

$$2x^{6}-4x^{3}x^{3}\times 2$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 3 ni qo‘shib, 6 ni oling.

$$2x^{6}-4x^{6}\times 2$$

8 hosil qilish uchun 4 va 2 ni ko'paytirish.

$$2x^{6}-8x^{6}$$

-6x^{6} ni olish uchun 2x^{6} va -8x^{6} ni birlashtirish.

$$-6x^{6}$$

x ga nisbatan hosilani topish

$$-36x^{5}$$

Derivativ ifodasidan foydalanish qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x^{4}\times 4}{10}x^{2}-\frac{16x^{3}}{4}x^{2}\times 2x)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x^{4}\times 4}{10}x^{2}-\frac{16x^{3}}{4}x^{3}\times 2)$$

20 hosil qilish uchun 5 va 4 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{20x^{4}}{10}x^{2}-\frac{16x^{3}}{4}x^{3}\times 2)$$

2x^{4} ni olish uchun 20x^{4} ni 10 ga bo‘ling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{4}x^{2}-\frac{16x^{3}}{4}x^{3}\times 2)$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va 2 ni qo‘shib, 6 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{6}-\frac{16x^{3}}{4}x^{3}\times 2)$$

4x^{3} ni olish uchun 16x^{3} ni 4 ga bo‘ling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{6}-4x^{3}x^{3}\times 2)$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 3 va 3 ni qo‘shib, 6 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{6}-4x^{6}\times 2)$$

8 hosil qilish uchun 4 va 2 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{6}-8x^{6})$$

-6x^{6} ni olish uchun 2x^{6} va -8x^{6} ni birlashtirish.

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

ax^{n} hosilasi – nax^{n-1}.

$$6\left(-6\right)x^{6-1}$$

6 ni -6 marotabaga ko'paytirish.

$$-36x^{6-1}$$

6 dan 1 ni ayirish.

$$-36x^{5}$$