(x^3+4x^2-10x+7)+(-6x^3+5x-10) eching

$$( { x }^{ 3 } +4 { x }^{ 2 } -10x+7)+(-6 { x }^{ 3 } +5x-10)$$

Baholash

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

Yechim qadamlari

-5x^{3} ni olish uchun x^{3} va -6x^{3} ni birlashtirish.

$$-5x^{3}+4x^{2}-10x+7+5x-10$$

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

$$-5x^{3}+4x^{2}-5x+7-10$$

-3 olish uchun 7 dan 10 ni ayirish.

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

x ga nisbatan hosilani topish

$$-15x^{2}+8x-5$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

-5x^{3} ni olish uchun x^{3} va -6x^{3} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-5x^{3}+4x^{2}-10x+7+5x-10)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-5x^{3}+4x^{2}-5x+7-10)$$

-3 olish uchun 7 dan 10 ni ayirish.

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

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

$$3\left(-5\right)x^{3-1}+2\times 4x^{2-1}-5x^{1-1}$$

3 ni -5 marotabaga ko'paytirish.

$$-15x^{3-1}+2\times 4x^{2-1}-5x^{1-1}$$

3 dan 1 ni ayirish.

$$-15x^{2}+2\times 4x^{2-1}-5x^{1-1}$$

2 ni 4 marotabaga ko'paytirish.

$$-15x^{2}+8x^{2-1}-5x^{1-1}$$

2 dan 1 ni ayirish.

$$-15x^{2}+8x^{1}-5x^{1-1}$$

1 dan 1 ni ayirish.

$$-15x^{2}+8x^{1}-5x^{0}$$

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

$$-15x^{2}+8x-5x^{0}$$

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

$$-15x^{2}+8x-5$$