(n+9)+(4n^3+2n^2+4n+2) eching

$$( n + 9 ) + ( 4 n ^ { 3 } + 2 n ^ { 2 } + 4 n + 2 )$$

Baholash

$$4n^{3}+2n^{2}+5n+11$$

Yechim qadamlari

5n ni olish uchun n va 4n ni birlashtirish.

$$5n+9+4n^{3}+2n^{2}+2$$

11 olish uchun 9 va 2'ni qo'shing.

$$5n+11+4n^{3}+2n^{2}$$

n ga nisbatan hosilani topish

$$12n^{2}+4n+5$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

5n ni olish uchun n va 4n ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}n}(5n+9+4n^{3}+2n^{2}+2)$$

11 olish uchun 9 va 2'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}n}(5n+11+4n^{3}+2n^{2})$$

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

$$5n^{1-1}+3\times 4n^{3-1}+2\times 2n^{2-1}$$

1 dan 1 ni ayirish.

$$5n^{0}+3\times 4n^{3-1}+2\times 2n^{2-1}$$

3 ni 4 marotabaga ko'paytirish.

$$5n^{0}+12n^{3-1}+2\times 2n^{2-1}$$

3 dan 1 ni ayirish.

$$5n^{0}+12n^{2}+2\times 2n^{2-1}$$

3 ni 4 marotabaga ko'paytirish.

$$5n^{0}+12n^{2}+4n^{2-1}$$

2 dan 1 ni ayirish.

$$5n^{0}+12n^{2}+4n^{1}$$

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

$$5n^{0}+12n^{2}+4n$$

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

$$5\times 1+12n^{2}+4n$$

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

$$5+12n^{2}+4n$$