(8h^3+2h^2+3h+5)+(h^3+7h) eching

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

Baholash

$$9h^{3}+2h^{2}+10h+5$$

Yechim qadamlari

9h^{3} ni olish uchun 8h^{3} va h^{3} ni birlashtirish.

$$9h^{3}+2h^{2}+3h+5+7h$$

10h ni olish uchun 3h va 7h ni birlashtirish.

$$9h^{3}+2h^{2}+10h+5$$

h ga nisbatan hosilani topish

$$27h^{2}+4h+10$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

9h^{3} ni olish uchun 8h^{3} va h^{3} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}h}(9h^{3}+2h^{2}+3h+5+7h)$$

10h ni olish uchun 3h va 7h ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}h}(9h^{3}+2h^{2}+10h+5)$$

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

$$3\times 9h^{3-1}+2\times 2h^{2-1}+10h^{1-1}$$

3 ni 9 marotabaga ko'paytirish.

$$27h^{3-1}+2\times 2h^{2-1}+10h^{1-1}$$

3 dan 1 ni ayirish.

$$27h^{2}+2\times 2h^{2-1}+10h^{1-1}$$

2 ni 2 marotabaga ko'paytirish.

$$27h^{2}+4h^{2-1}+10h^{1-1}$$

2 dan 1 ni ayirish.

$$27h^{2}+4h^{1}+10h^{1-1}$$

1 dan 1 ni ayirish.

$$27h^{2}+4h^{1}+10h^{0}$$

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

$$27h^{2}+4h+10h^{0}$$

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

$$27h^{2}+4h+10\times 1$$

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

$$27h^{2}+4h+10$$