(6x^3+3x^2+3)+(2x^3-5x+1) eching

$$( 6 x ^ { 3 } + 3 x ^ { 2 } + 3 ) + ( 2 x ^ { 3 } - 5 x + 1 )$$

Baholash

$$8x^{3}+3x^{2}-5x+4$$

Yechim qadamlari

8x^{3} ni olish uchun 6x^{3} va 2x^{3} ni birlashtirish.

$$8x^{3}+3x^{2}+3-5x+1$$

4 olish uchun 3 va 1'ni qo'shing.

$$8x^{3}+3x^{2}+4-5x$$

x ga nisbatan hosilani topish

$$24x^{2}+6x-5$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

8x^{3} ni olish uchun 6x^{3} va 2x^{3} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{3}+3x^{2}+3-5x+1)$$

4 olish uchun 3 va 1'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{3}+3x^{2}+4-5x)$$

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

$$3\times 8x^{3-1}+2\times 3x^{2-1}-5x^{1-1}$$

3 ni 8 marotabaga ko'paytirish.

$$24x^{3-1}+2\times 3x^{2-1}-5x^{1-1}$$

3 dan 1 ni ayirish.

$$24x^{2}+2\times 3x^{2-1}-5x^{1-1}$$

2 ni 3 marotabaga ko'paytirish.

$$24x^{2}+6x^{2-1}-5x^{1-1}$$

2 dan 1 ni ayirish.

$$24x^{2}+6x^{1}-5x^{1-1}$$

1 dan 1 ni ayirish.

$$24x^{2}+6x^{1}-5x^{0}$$

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

$$24x^{2}+6x-5x^{0}$$

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

$$24x^{2}+6x-5$$