(-8+4x^{2}+4xy^2)+(9x^3-x^2+xy^2) eching

$$( - 8 + 4 x ^ { 2 } + 4 x y ^ { 2 } ) + ( 9 x ^ { 3 } - x ^ { 2 } + x y ^ { 2 } )$$

x ga nisbatan hosilani topish

$$27x^{2}+6x+5y^{2}$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(-8+3x^{2}+4xy^{2}+9x^{3}+xy^{2})$$

5xy^{2} ni olish uchun 4xy^{2} va xy^{2} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-8+3x^{2}+5xy^{2}+9x^{3})$$

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

$$2\times 3x^{2-1}+5y^{2}x^{1-1}+3\times 9x^{3-1}$$

2 ni 3 marotabaga ko'paytirish.

$$6x^{2-1}+5y^{2}x^{1-1}+3\times 9x^{3-1}$$

2 dan 1 ni ayirish.

$$6x^{1}+5y^{2}x^{1-1}+3\times 9x^{3-1}$$

1 dan 1 ni ayirish.

$$6x^{1}+5y^{2}x^{0}+3\times 9x^{3-1}$$

1 ni 5y^{2} marotabaga ko'paytirish.

$$6x^{1}+5y^{2}x^{0}+27x^{3-1}$$

3 dan 1 ni ayirish.

$$6x^{1}+5y^{2}x^{0}+27x^{2}$$

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

$$6x+5y^{2}x^{0}+27x^{2}$$

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

$$6x+5y^{2}\times 1+27x^{2}$$

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

$$6x+5y^{2}+27x^{2}$$

Baholash

$$9x^{3}+3x^{2}+5xy^{2}-8$$