(15x^3+8x)+(2x^2-6x+9) eching

$$(15 { x }^{ 3 } +8x)+(2 { x }^{ 2 } -6x+9)$$

x ga nisbatan hosilani topish

$$45x^{2}+4x+2$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

2x ni olish uchun 8x va -6x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15x^{3}+2x+2x^{2}+9)$$

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

$$3\times 15x^{3-1}+2x^{1-1}+2\times 2x^{2-1}$$

3 ni 15 marotabaga ko'paytirish.

$$45x^{3-1}+2x^{1-1}+2\times 2x^{2-1}$$

3 dan 1 ni ayirish.

$$45x^{2}+2x^{1-1}+2\times 2x^{2-1}$$

1 dan 1 ni ayirish.

$$45x^{2}+2x^{0}+2\times 2x^{2-1}$$

1 ni 2 marotabaga ko'paytirish.

$$45x^{2}+2x^{0}+4x^{2-1}$$

2 dan 1 ni ayirish.

$$45x^{2}+2x^{0}+4x^{1}$$

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

$$45x^{2}+2x^{0}+4x$$

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

$$45x^{2}+2\times 1+4x$$

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

$$45x^{2}+2+4x$$

Baholash

$$15x^{3}+2x^{2}+2x+9$$

Yechim qadamlari

2x ni olish uchun 8x va -6x ni birlashtirish.

$$15x^{3}+2x+2x^{2}+9$$