(2m^3+m^2+8m+9)+(9m^3-5m^2+4m+6) eching

$$( 2 m ^ { 3 } + m ^ { 2 } + 8 m + 9 ) + ( 9 m ^ { 3 } - 5 m ^ { 2 } + 4 m + 6 )$$

Baholash

$$11m^{3}-4m^{2}+12m+15$$

Yechim qadamlari

11m^{3} ni olish uchun 2m^{3} va 9m^{3} ni birlashtirish.

$$11m^{3}+m^{2}+8m+9-5m^{2}+4m+6$$

-4m^{2} ni olish uchun m^{2} va -5m^{2} ni birlashtirish.

$$11m^{3}-4m^{2}+8m+9+4m+6$$

12m ni olish uchun 8m va 4m ni birlashtirish.

$$11m^{3}-4m^{2}+12m+9+6$$

15 olish uchun 9 va 6'ni qo'shing.

$$11m^{3}-4m^{2}+12m+15$$

m ga nisbatan hosilani topish

$$33m^{2}-8m+12$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

11m^{3} ni olish uchun 2m^{3} va 9m^{3} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}m}(11m^{3}+m^{2}+8m+9-5m^{2}+4m+6)$$

-4m^{2} ni olish uchun m^{2} va -5m^{2} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}m}(11m^{3}-4m^{2}+8m+9+4m+6)$$

12m ni olish uchun 8m va 4m ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}m}(11m^{3}-4m^{2}+12m+9+6)$$

15 olish uchun 9 va 6'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}m}(11m^{3}-4m^{2}+12m+15)$$

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

$$3\times 11m^{3-1}+2\left(-4\right)m^{2-1}+12m^{1-1}$$

3 ni 11 marotabaga ko'paytirish.

$$33m^{3-1}+2\left(-4\right)m^{2-1}+12m^{1-1}$$

3 dan 1 ni ayirish.

$$33m^{2}+2\left(-4\right)m^{2-1}+12m^{1-1}$$

2 ni -4 marotabaga ko'paytirish.

$$33m^{2}-8m^{2-1}+12m^{1-1}$$

2 dan 1 ni ayirish.

$$33m^{2}-8m^{1}+12m^{1-1}$$

1 dan 1 ni ayirish.

$$33m^{2}-8m^{1}+12m^{0}$$

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

$$33m^{2}-8m+12m^{0}$$

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

$$33m^{2}-8m+12\times 1$$

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

$$33m^{2}-8m+12$$