x^3-3x+1x^5+4x^3+x^2+3x+1 eching

$$x ^ { 3 } - 3 x + 1 x ^ { 5 } + 4 x ^ { 3 } + x ^ { 2 } + 3 x + 1$$

Baholash

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

Yechim qadamlari

5x^{3} ni olish uchun x^{3} va 4x^{3} ni birlashtirish.

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

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

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

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

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

x ga nisbatan hosilani topish

$$x\left(5x^{3}+15x+2\right)$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

5x^{3} ni olish uchun x^{3} va 4x^{3} ni birlashtirish.

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

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

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

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

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

3 ni 5 marotabaga ko'paytirish.

$$15x^{3-1}+5x^{5-1}+2x^{2-1}$$

3 dan 1 ni ayirish.

$$15x^{2}+5x^{5-1}+2x^{2-1}$$

5 dan 1 ni ayirish.

$$15x^{2}+5x^{4}+2x^{2-1}$$

2 dan 1 ni ayirish.

$$15x^{2}+5x^{4}+2x^{1}$$

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

$$15x^{2}+5x^{4}+2x$$