x^2+2xx^3-2xx^2-4 eching

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

Baholash

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

Yechim qadamlari

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

$$x^{2}+2x^{4}-2xx^{2}-4$$

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

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

x ga nisbatan hosilani topish

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

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+2x^{4}-2xx^{2}-4)$$

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

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

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

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

2 dan 1 ni ayirish.

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

4 ni 2 marotabaga ko'paytirish.

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

4 dan 1 ni ayirish.

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

4 ni 2 marotabaga ko'paytirish.

$$2x^{1}+8x^{3}-6x^{3-1}$$

3 dan 1 ni ayirish.

$$2x^{1}+8x^{3}-6x^{2}$$

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

$$2x+8x^{3}-6x^{2}$$