(3y^3+6y-5)+(3y^2-5y+1) eching

$$( 3 y ^ { 3 } + 6 y - 5 ) + ( 3 y ^ { 2 } - 5 y + 1 )$$

Baholash

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

Yechim qadamlari

y ni olish uchun 6y va -5y ni birlashtirish.

$$3y^{3}+y-5+3y^{2}+1$$

-4 olish uchun -5 va 1'ni qo'shing.

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

y ga nisbatan hosilani topish

$$\left(3y+1\right)^{2}$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

y ni olish uchun 6y va -5y ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}y}(3y^{3}+y-5+3y^{2}+1)$$

-4 olish uchun -5 va 1'ni qo'shing.

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

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

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

3 ni 3 marotabaga ko'paytirish.

$$9y^{3-1}+y^{1-1}+2\times 3y^{2-1}$$

3 dan 1 ni ayirish.

$$9y^{2}+y^{1-1}+2\times 3y^{2-1}$$

1 dan 1 ni ayirish.

$$9y^{2}+y^{0}+2\times 3y^{2-1}$$

1 ni 1 marotabaga ko'paytirish.

$$9y^{2}+y^{0}+6y^{2-1}$$

2 dan 1 ni ayirish.

$$9y^{2}+y^{0}+6y^{1}$$

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

$$9y^{2}+y^{0}+6y$$

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

$$9y^{2}+1+6y$$