(6x^4+2x^3-x+5)+(-2x^4+x^3+4x-10) eching

$$( 6 x ^ { 4 } + 2 x ^ { 3 } - x + 5 ) + ( - 2 x ^ { 4 } + x ^ { 3 } + 4 x - 10 )$$

Baholash

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

Yechim qadamlari

4x^{4} ni olish uchun 6x^{4} va -2x^{4} ni birlashtirish.

$$4x^{4}+2x^{3}-x+5+x^{3}+4x-10$$

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

$$4x^{4}+3x^{3}-x+5+4x-10$$

3x ni olish uchun -x va 4x ni birlashtirish.

$$4x^{4}+3x^{3}+3x+5-10$$

-5 olish uchun 5 dan 10 ni ayirish.

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

x ga nisbatan hosilani topish

$$16x^{3}+9x^{2}+3$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

4x^{4} ni olish uchun 6x^{4} va -2x^{4} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{4}+2x^{3}-x+5+x^{3}+4x-10)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{4}+3x^{3}-x+5+4x-10)$$

3x ni olish uchun -x va 4x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{4}+3x^{3}+3x+5-10)$$

-5 olish uchun 5 dan 10 ni ayirish.

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

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

$$4\times 4x^{4-1}+3\times 3x^{3-1}+3x^{1-1}$$

4 ni 4 marotabaga ko'paytirish.

$$16x^{4-1}+3\times 3x^{3-1}+3x^{1-1}$$

4 dan 1 ni ayirish.

$$16x^{3}+3\times 3x^{3-1}+3x^{1-1}$$

3 ni 3 marotabaga ko'paytirish.

$$16x^{3}+9x^{3-1}+3x^{1-1}$$

3 dan 1 ni ayirish.

$$16x^{3}+9x^{2}+3x^{1-1}$$

1 dan 1 ni ayirish.

$$16x^{3}+9x^{2}+3x^{0}$$

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

$$16x^{3}+9x^{2}+3\times 1$$

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

$$16x^{3}+9x^{2}+3$$