(4x^3-3x^2+7x-2)+(x^3+7x^2-4x+5) eching

$$( 4 x ^ { 3 } - 3 x ^ { 2 } + 7 x - 2 ) + ( x ^ { 3 } + 7 x ^ { 2 } - 4 x + 5 )$$

Baholash

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

Yechim qadamlari

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

$$5x^{3}-3x^{2}+7x-2+7x^{2}-4x+5$$

4x^{2} ni olish uchun -3x^{2} va 7x^{2} ni birlashtirish.

$$5x^{3}+4x^{2}+7x-2-4x+5$$

3x ni olish uchun 7x va -4x ni birlashtirish.

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

3 olish uchun -2 va 5'ni qo'shing.

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

x ga nisbatan hosilani topish

$$15x^{2}+8x+3$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{3}-3x^{2}+7x-2+7x^{2}-4x+5)$$

4x^{2} ni olish uchun -3x^{2} va 7x^{2} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{3}+4x^{2}+7x-2-4x+5)$$

3x ni olish uchun 7x va -4x ni birlashtirish.

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

3 olish uchun -2 va 5'ni qo'shing.

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

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

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

3 ni 5 marotabaga ko'paytirish.

$$15x^{3-1}+2\times 4x^{2-1}+3x^{1-1}$$

3 dan 1 ni ayirish.

$$15x^{2}+2\times 4x^{2-1}+3x^{1-1}$$

2 ni 4 marotabaga ko'paytirish.

$$15x^{2}+8x^{2-1}+3x^{1-1}$$

2 dan 1 ni ayirish.

$$15x^{2}+8x^{1}+3x^{1-1}$$

1 dan 1 ni ayirish.

$$15x^{2}+8x^{1}+3x^{0}$$

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

$$15x^{2}+8x+3x^{0}$$

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

$$15x^{2}+8x+3\times 1$$

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

$$15x^{2}+8x+3$$