x^4+3x^3-x-3x^3+x^2-5x+3 eching

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

Baholash

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

Yechim qadamlari

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

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

-6x ni olish uchun -x va -5x ni birlashtirish.

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

x ga nisbatan hosilani topish

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

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

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

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

-6x ni olish uchun -x va -5x ni birlashtirish.

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

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

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

4 dan 1 ni ayirish.

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

1 dan 1 ni ayirish.

$$4x^{3}-6x^{0}+2x^{2-1}$$

2 dan 1 ni ayirish.

$$4x^{3}-6x^{0}+2x^{1}$$

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

$$4x^{3}-6x^{0}+2x$$

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

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