(-2x^3+5x^2-5x+7)+(7x^3+10x^2-10x-3) eching

$$( - 2 x ^ { 3 } + 5 x ^ { 2 } - 5 x + 7 ) + ( 7 x ^ { 3 } + 10 x ^ { 2 } - 10 x - 3 )$$

Baholash

$$5x^{3}+15x^{2}-15x+4$$

Yechim qadamlari

5x^{3} ni olish uchun -2x^{3} va 7x^{3} ni birlashtirish.

$$5x^{3}+5x^{2}-5x+7+10x^{2}-10x-3$$

15x^{2} ni olish uchun 5x^{2} va 10x^{2} ni birlashtirish.

$$5x^{3}+15x^{2}-5x+7-10x-3$$

-15x ni olish uchun -5x va -10x ni birlashtirish.

$$5x^{3}+15x^{2}-15x+7-3$$

4 olish uchun 7 dan 3 ni ayirish.

$$5x^{3}+15x^{2}-15x+4$$

x ga nisbatan hosilani topish

$$15\left(x^{2}+2x-1\right)$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

5x^{3} ni olish uchun -2x^{3} va 7x^{3} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{3}+5x^{2}-5x+7+10x^{2}-10x-3)$$

15x^{2} ni olish uchun 5x^{2} va 10x^{2} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{3}+15x^{2}-5x+7-10x-3)$$

-15x ni olish uchun -5x va -10x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{3}+15x^{2}-15x+7-3)$$

4 olish uchun 7 dan 3 ni ayirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{3}+15x^{2}-15x+4)$$

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

$$3\times 5x^{3-1}+2\times 15x^{2-1}-15x^{1-1}$$

3 ni 5 marotabaga ko'paytirish.

$$15x^{3-1}+2\times 15x^{2-1}-15x^{1-1}$$

3 dan 1 ni ayirish.

$$15x^{2}+2\times 15x^{2-1}-15x^{1-1}$$

2 ni 15 marotabaga ko'paytirish.

$$15x^{2}+30x^{2-1}-15x^{1-1}$$

2 dan 1 ni ayirish.

$$15x^{2}+30x^{1}-15x^{1-1}$$

1 dan 1 ni ayirish.

$$15x^{2}+30x^{1}-15x^{0}$$

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

$$15x^{2}+30x-15x^{0}$$

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

$$15x^{2}+30x-15$$