(3y^3-2y^2-7y)+(-4y^2+2y-5) eching

$$( 3 y ^ { 3 } - 2 y ^ { 2 } - 7 y ) + ( - 4 y ^ { 2 } + 2 y - 5 )$$

Baholash

$$3y^{3}-6y^{2}-5y-5$$

Yechim qadamlari

-6y^{2} ni olish uchun -2y^{2} va -4y^{2} ni birlashtirish.

$$3y^{3}-6y^{2}-7y+2y-5$$

-5y ni olish uchun -7y va 2y ni birlashtirish.

$$3y^{3}-6y^{2}-5y-5$$

y ga nisbatan hosilani topish

$$\left(3y-5\right)\left(3y+1\right)$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

-6y^{2} ni olish uchun -2y^{2} va -4y^{2} ni birlashtirish.

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

-5y ni olish uchun -7y va 2y ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}y}(3y^{3}-6y^{2}-5y-5)$$

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

$$3\times 3y^{3-1}+2\left(-6\right)y^{2-1}-5y^{1-1}$$

3 ni 3 marotabaga ko'paytirish.

$$9y^{3-1}+2\left(-6\right)y^{2-1}-5y^{1-1}$$

3 dan 1 ni ayirish.

$$9y^{2}+2\left(-6\right)y^{2-1}-5y^{1-1}$$

2 ni -6 marotabaga ko'paytirish.

$$9y^{2}-12y^{2-1}-5y^{1-1}$$

2 dan 1 ni ayirish.

$$9y^{2}-12y^{1}-5y^{1-1}$$

1 dan 1 ni ayirish.

$$9y^{2}-12y^{1}-5y^{0}$$

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

$$9y^{2}-12y-5y^{0}$$

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

$$9y^{2}-12y-5$$