4x^6+2x^4-x^2divx+1 eching

$$4 x ^ { 6 } + 2 x ^ { 4 } - x ^ { 2 } \div x + 1$$

Baholash

$$4x^{6}+2x^{4}-x+1$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun maxrajning darajasini surat darajasidan ayiring. 2 dan 1 ni ayirib, 1 ni oling.

$$4x^{6}+2x^{4}-x^{1}+1$$

1 daraja ko‘rsatkichini x ga hisoblang va x ni qiymatni oling.

$$4x^{6}+2x^{4}-x+1$$

x ga nisbatan hosilani topish

$$24x^{5}+8x^{3}-1$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun maxrajning darajasini surat darajasidan ayiring. 2 dan 1 ni ayirib, 1 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{6}+2x^{4}-x^{1}+1)$$

1 daraja ko‘rsatkichini x ga hisoblang va x ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{6}+2x^{4}-x+1)$$

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

$$6\times 4x^{6-1}+4\times 2x^{4-1}-x^{1-1}$$

6 ni 4 marotabaga ko'paytirish.

$$24x^{6-1}+4\times 2x^{4-1}-x^{1-1}$$

6 dan 1 ni ayirish.

$$24x^{5}+4\times 2x^{4-1}-x^{1-1}$$

4 ni 2 marotabaga ko'paytirish.

$$24x^{5}+8x^{4-1}-x^{1-1}$$

4 dan 1 ni ayirish.

$$24x^{5}+8x^{3}-x^{1-1}$$

1 dan 1 ni ayirish.

$$24x^{5}+8x^{3}-x^{0}$$

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

$$24x^{5}+8x^{3}-1$$