2x^3-x^2+3x-6+4x^2+x+4 eching

$$2 { x }^{ 3 } - { x }^{ 2 } +3x-6+4 { x }^{ 2 } +x+4$$

Baholash

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

Yechim qadamlari

3x^{2} ni olish uchun -x^{2} va 4x^{2} ni birlashtirish.

$$2x^{3}+3x^{2}+3x-6+x+4$$

4x ni olish uchun 3x va x ni birlashtirish.

$$2x^{3}+3x^{2}+4x-6+4$$

-2 olish uchun -6 va 4'ni qo'shing.

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

x ga nisbatan hosilani topish

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

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

3x^{2} ni olish uchun -x^{2} va 4x^{2} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+3x^{2}+3x-6+x+4)$$

4x ni olish uchun 3x va x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+3x^{2}+4x-6+4)$$

-2 olish uchun -6 va 4'ni qo'shing.

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

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

$$3\times 2x^{3-1}+2\times 3x^{2-1}+4x^{1-1}$$

3 ni 2 marotabaga ko'paytirish.

$$6x^{3-1}+2\times 3x^{2-1}+4x^{1-1}$$

3 dan 1 ni ayirish.

$$6x^{2}+2\times 3x^{2-1}+4x^{1-1}$$

2 ni 3 marotabaga ko'paytirish.

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

2 dan 1 ni ayirish.

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

1 dan 1 ni ayirish.

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

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

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

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

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

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

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