2x^4-x^3+9x^2quadx^2+4 eching

$$2 x ^ { 4 } - x ^ { 3 } + 9 x ^ { 2 } \quad x ^ { 2 } + 4$$

Baholash

$$11x^{4}-x^{3}+4$$

Yechim qadamlari

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

$$2x^{4}-x^{3}+9x^{4}+4$$

11x^{4} ni olish uchun 2x^{4} va 9x^{4} ni birlashtirish.

$$11x^{4}-x^{3}+4$$

x ga nisbatan hosilani topish

$$\left(44x-3\right)x^{2}$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

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

$$4\times 2x^{4-1}+3\left(-1\right)x^{3-1}+2\times 9x^{2}x^{2-1}$$

4 ni 2 marotabaga ko'paytirish.

$$8x^{4-1}+3\left(-1\right)x^{3-1}+2\times 9x^{2}x^{2-1}$$

4 dan 1 ni ayirish.

$$8x^{3}+3\left(-1\right)x^{3-1}+2\times 9x^{2}x^{2-1}$$

3 ni -1 marotabaga ko'paytirish.

$$8x^{3}-3x^{3-1}+2\times 9x^{2}x^{2-1}$$

3 dan 1 ni ayirish.

$$8x^{3}-3x^{2}+2\times 9x^{2}x^{2-1}$$

3 ni -1 marotabaga ko'paytirish.

$$8x^{3}-3x^{2}+18x^{2}x^{2-1}$$

2 dan 1 ni ayirish.

$$8x^{3}-3x^{2}+18x^{2}x^{1}$$

Har qanday t sharti uchun t^{1}=t.

$$8x^{3}-3x^{2}+18x^{2}x$$