(4x^3+2x^2-11x+3)+(7x^3-5x^2-9x) eching

$$( 4 x ^ { 3 } + 2 x ^ { 2 } - 11 x + 3 ) + ( 7 x ^ { 3 } - 5 x ^ { 2 } - 9 x )$$

Baholash

$$11x^{3}-3x^{2}-20x+3$$

Yechim qadamlari

11x^{3} ni olish uchun 4x^{3} va 7x^{3} ni birlashtirish.

$$11x^{3}+2x^{2}-11x+3-5x^{2}-9x$$

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

$$11x^{3}-3x^{2}-11x+3-9x$$

-20x ni olish uchun -11x va -9x ni birlashtirish.

$$11x^{3}-3x^{2}-20x+3$$

x ga nisbatan hosilani topish

$$33x^{2}-6x-20$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

11x^{3} ni olish uchun 4x^{3} va 7x^{3} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{3}+2x^{2}-11x+3-5x^{2}-9x)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{3}-3x^{2}-11x+3-9x)$$

-20x ni olish uchun -11x va -9x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(11x^{3}-3x^{2}-20x+3)$$

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

$$3\times 11x^{3-1}+2\left(-3\right)x^{2-1}-20x^{1-1}$$

3 ni 11 marotabaga ko'paytirish.

$$33x^{3-1}+2\left(-3\right)x^{2-1}-20x^{1-1}$$

3 dan 1 ni ayirish.

$$33x^{2}+2\left(-3\right)x^{2-1}-20x^{1-1}$$

2 ni -3 marotabaga ko'paytirish.

$$33x^{2}-6x^{2-1}-20x^{1-1}$$

2 dan 1 ni ayirish.

$$33x^{2}-6x^{1}-20x^{1-1}$$

1 dan 1 ni ayirish.

$$33x^{2}-6x^{1}-20x^{0}$$

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

$$33x^{2}-6x-20x^{0}$$

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

$$33x^{2}-6x-20$$