2x^{2}-x^3+3x^3-x-x^3+4x+3-5x^2= eching

$$2 x ^ { 2 } - x ^ { 3 } + 3 x ^ { 3 } - x - x ^ { 3 } + 4 x + 3 - 5 x ^ { 2 } =$$

Baholash

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

Yechim qadamlari

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

$$2x^{2}+2x^{3}-x-x^{3}+4x+3-5x^{2}$$

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

$$2x^{2}+x^{3}-x+4x+3-5x^{2}$$

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

$$2x^{2}+x^{3}+3x+3-5x^{2}$$

-3x^{2} ni olish uchun 2x^{2} va -5x^{2} ni birlashtirish.

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

x ga nisbatan hosilani topish

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

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}+2x^{3}-x-x^{3}+4x+3-5x^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}+x^{3}-x+4x+3-5x^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}+x^{3}+3x+3-5x^{2})$$

-3x^{2} ni olish uchun 2x^{2} va -5x^{2} ni birlashtirish.

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

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

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

2 ni -3 marotabaga ko'paytirish.

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

2 dan 1 ni ayirish.

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

3 dan 1 ni ayirish.

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

1 dan 1 ni ayirish.

$$-6x^{1}+3x^{2}+3x^{0}$$

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

$$-6x+3x^{2}+3x^{0}$$

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

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

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

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