(7y^3+y^2+6y+8)+(6y^3+5y^2+y+7) eching

$$( 7 y ^ { 3 } + y ^ { 2 } + 6 y + 8 ) + ( 6 y ^ { 3 } + 5 y ^ { 2 } + y + 7 )$$

Baholash

$$13y^{3}+6y^{2}+7y+15$$

Yechim qadamlari

13y^{3} ni olish uchun 7y^{3} va 6y^{3} ni birlashtirish.

$$13y^{3}+y^{2}+6y+8+5y^{2}+y+7$$

6y^{2} ni olish uchun y^{2} va 5y^{2} ni birlashtirish.

$$13y^{3}+6y^{2}+6y+8+y+7$$

7y ni olish uchun 6y va y ni birlashtirish.

$$13y^{3}+6y^{2}+7y+8+7$$

15 olish uchun 8 va 7'ni qo'shing.

$$13y^{3}+6y^{2}+7y+15$$

y ga nisbatan hosilani topish

$$39y^{2}+12y+7$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

13y^{3} ni olish uchun 7y^{3} va 6y^{3} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}y}(13y^{3}+y^{2}+6y+8+5y^{2}+y+7)$$

6y^{2} ni olish uchun y^{2} va 5y^{2} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}y}(13y^{3}+6y^{2}+6y+8+y+7)$$

7y ni olish uchun 6y va y ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}y}(13y^{3}+6y^{2}+7y+8+7)$$

15 olish uchun 8 va 7'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}y}(13y^{3}+6y^{2}+7y+15)$$

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

$$3\times 13y^{3-1}+2\times 6y^{2-1}+7y^{1-1}$$

3 ni 13 marotabaga ko'paytirish.

$$39y^{3-1}+2\times 6y^{2-1}+7y^{1-1}$$

3 dan 1 ni ayirish.

$$39y^{2}+2\times 6y^{2-1}+7y^{1-1}$$

2 ni 6 marotabaga ko'paytirish.

$$39y^{2}+12y^{2-1}+7y^{1-1}$$

2 dan 1 ni ayirish.

$$39y^{2}+12y^{1}+7y^{1-1}$$

1 dan 1 ni ayirish.

$$39y^{2}+12y^{1}+7y^{0}$$

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

$$39y^{2}+12y+7y^{0}$$

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

$$39y^{2}+12y+7\times 1$$

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

$$39y^{2}+12y+7$$