=10+20x-2x^2+10x^2-40x+5 eching

$$= 10 + 20 x - 2 x ^ { 2 } + 10 x ^ { 2 } - 40 x + 5$$

Baholash

$$8x^{2}-20x+15$$

Yechim qadamlari

8x^{2} ni olish uchun -2x^{2} va 10x^{2} ni birlashtirish.

$$10+20x+8x^{2}-40x+5$$

-20x ni olish uchun 20x va -40x ni birlashtirish.

$$10-20x+8x^{2}+5$$

15 olish uchun 10 va 5'ni qo'shing.

$$15-20x+8x^{2}$$

x ga nisbatan hosilani topish

$$16x-20$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

8x^{2} ni olish uchun -2x^{2} va 10x^{2} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10+20x+8x^{2}-40x+5)$$

-20x ni olish uchun 20x va -40x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10-20x+8x^{2}+5)$$

15 olish uchun 10 va 5'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15-20x+8x^{2})$$

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

$$-20x^{1-1}+2\times 8x^{2-1}$$

1 dan 1 ni ayirish.

$$-20x^{0}+2\times 8x^{2-1}$$

2 ni 8 marotabaga ko'paytirish.

$$-20x^{0}+16x^{2-1}$$

2 dan 1 ni ayirish.

$$-20x^{0}+16x^{1}$$

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

$$-20x^{0}+16x$$

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

$$-20+16x$$