x^3+1x^3+x^2+x+1x^2+x+1 eching

$${ x }^{ 3 } +1 { x }^{ 3 } + { x }^{ 2 } +x+1 { x }^{ 2 } +x+1$$

Baholash

$$2x^{3}+2x^{2}+2x+1$$

Yechim qadamlari

2x^{3} ni olish uchun x^{3} va 1x^{3} ni birlashtirish.

$$2x^{3}+x^{2}+x+1x^{2}+x+1$$

2x^{2} ni olish uchun x^{2} va 1x^{2} ni birlashtirish.

$$2x^{3}+2x^{2}+x+x+1$$

2x ni olish uchun x va x ni birlashtirish.

$$2x^{3}+2x^{2}+2x+1$$

x ga nisbatan hosilani topish

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

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

2x^{3} ni olish uchun x^{3} va 1x^{3} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+x^{2}+x+1x^{2}+x+1)$$

2x^{2} ni olish uchun x^{2} va 1x^{2} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+2x^{2}+x+x+1)$$

2x ni olish uchun x va x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+2x^{2}+2x+1)$$

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

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

3 ni 2 marotabaga ko'paytirish.

$$6x^{3-1}+2\times 2x^{2-1}+2x^{1-1}$$

3 dan 1 ni ayirish.

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

2 ni 2 marotabaga ko'paytirish.

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

2 dan 1 ni ayirish.

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

1 dan 1 ni ayirish.

$$6x^{2}+4x^{1}+2x^{0}$$

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

$$6x^{2}+4x+2x^{0}$$

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

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

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

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