3x^3-2x^2+5x-7-4x^2-3x+2 eching

$$3 x ^ { 3 } - 2 x ^ { 2 } + 5 x - 7 - 4 x ^ { 2 } - 3 x + 2$$

Baholash

$$3x^{3}-6x^{2}+2x-5$$

Yechim qadamlari

-6x^{2} ni olish uchun -2x^{2} va -4x^{2} ni birlashtirish.

$$3x^{3}-6x^{2}+5x-7-3x+2$$

2x ni olish uchun 5x va -3x ni birlashtirish.

$$3x^{3}-6x^{2}+2x-7+2$$

-5 olish uchun -7 va 2'ni qo'shing.

$$3x^{3}-6x^{2}+2x-5$$

x ga nisbatan hosilani topish

$$9x^{2}-12x+2$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

-6x^{2} ni olish uchun -2x^{2} va -4x^{2} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{3}-6x^{2}+5x-7-3x+2)$$

2x ni olish uchun 5x va -3x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{3}-6x^{2}+2x-7+2)$$

-5 olish uchun -7 va 2'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{3}-6x^{2}+2x-5)$$

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

$$3\times 3x^{3-1}+2\left(-6\right)x^{2-1}+2x^{1-1}$$

3 ni 3 marotabaga ko'paytirish.

$$9x^{3-1}+2\left(-6\right)x^{2-1}+2x^{1-1}$$

3 dan 1 ni ayirish.

$$9x^{2}+2\left(-6\right)x^{2-1}+2x^{1-1}$$

2 ni -6 marotabaga ko'paytirish.

$$9x^{2}-12x^{2-1}+2x^{1-1}$$

2 dan 1 ni ayirish.

$$9x^{2}-12x^{1}+2x^{1-1}$$

1 dan 1 ni ayirish.

$$9x^{2}-12x^{1}+2x^{0}$$

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

$$9x^{2}-12x+2x^{0}$$

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

$$9x^{2}-12x+2\times 1$$

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

$$9x^{2}-12x+2$$