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

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

Baholash

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

Yechim qadamlari

12x^{2} ni olish uchun 5x^{2} va 7x^{2} ni birlashtirish.

$$12x^{2}+3x+6-2x+3$$

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

$$12x^{2}+x+6+3$$

9 olish uchun 6 va 3'ni qo'shing.

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

x ga nisbatan hosilani topish

$$24x+1$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

12x^{2} ni olish uchun 5x^{2} va 7x^{2} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{2}+3x+6-2x+3)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{2}+x+6+3)$$

9 olish uchun 6 va 3'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{2}+x+9)$$

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

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

2 ni 12 marotabaga ko'paytirish.

$$24x^{2-1}+x^{1-1}$$

2 dan 1 ni ayirish.

$$24x^{1}+x^{1-1}$$

1 dan 1 ni ayirish.

$$24x^{1}+x^{0}$$

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

$$24x+x^{0}$$

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

$$24x+1$$