-x(-5^3)(5*5^2)+(3*5)-1 eching

$$- x ( - 5 ^ { 3 } ) ( 5 \cdot 5 ^ { 2 } ) + ( 3 \cdot 5 ) - 1$$

Baholash

$$15625x+14$$

Yechim qadamlari

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

$$\left(-x\right)\left(-5^{3}\right)\times 5^{3}+3\times 5-1$$

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

$$\left(-x\right)\left(-125\right)\times 5^{3}+3\times 5-1$$

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

$$\left(-x\right)\left(-125\right)\times 125+3\times 5-1$$

-15625 hosil qilish uchun -125 va 125 ni ko'paytirish.

$$\left(-x\right)\left(-15625\right)+3\times 5-1$$

15 hosil qilish uchun 3 va 5 ni ko'paytirish.

$$\left(-x\right)\left(-15625\right)+15-1$$

14 olish uchun 15 dan 1 ni ayirish.

$$\left(-x\right)\left(-15625\right)+14$$

15625 hosil qilish uchun -1 va -15625 ni ko'paytirish.

$$15625x+14$$

x ga nisbatan hosilani topish

$$15625$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x\right)\left(-5^{3}\right)\times 5^{3}+3\times 5-1)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x\right)\left(-125\right)\times 5^{3}+3\times 5-1)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x\right)\left(-125\right)\times 125+3\times 5-1)$$

-15625 hosil qilish uchun -125 va 125 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x\right)\left(-15625\right)+3\times 5-1)$$

15 hosil qilish uchun 3 va 5 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x\right)\left(-15625\right)+15-1)$$

14 olish uchun 15 dan 1 ni ayirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-x\right)\left(-15625\right)+14)$$

15625 hosil qilish uchun -1 va -15625 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15625x+14)$$

Polinomialning hosilasi bu uning shartlari hosilasining yig‘indisiga teng. Konstant shartning hosilasi 0. ax^{n} ning hosilasi nax^{n-1}.

$$15625x^{1-1}$$

1 dan 1 ni ayirish.

$$15625x^{0}$$

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

$$15625\times 1$$

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

$$15625$$