(y+5)+(2y+4y^2-2) eching

$$( y + 5 ) + ( 2 y + 4 y ^ { 2 } - 2 )$$

Baholash

$$4y^{2}+3y+3$$

Yechim qadamlari

3y ni olish uchun y va 2y ni birlashtirish.

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

3 olish uchun 5 dan 2 ni ayirish.

$$3y+3+4y^{2}$$

y ga nisbatan hosilani topish

$$8y+3$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

3y ni olish uchun y va 2y ni birlashtirish.

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

3 olish uchun 5 dan 2 ni ayirish.

$$\frac{\mathrm{d}}{\mathrm{d}y}(3y+3+4y^{2})$$

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

$$3y^{1-1}+2\times 4y^{2-1}$$

1 dan 1 ni ayirish.

$$3y^{0}+2\times 4y^{2-1}$$

2 ni 4 marotabaga ko'paytirish.

$$3y^{0}+8y^{2-1}$$

2 dan 1 ni ayirish.

$$3y^{0}+8y^{1}$$

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

$$3y^{0}+8y$$

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

$$3\times 1+8y$$

Har qanday t sharti uchun t\times 1=t va 1t=t.

$$3+8y$$