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

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

Baholash

$$12x^{3}-x-5$$

Yechim qadamlari

12x^{3} ni olish uchun 7x^{3} va 5x^{3} ni birlashtirish.

$$12x^{3}-2-x-3$$

-5 olish uchun -2 dan 3 ni ayirish.

$$12x^{3}-5-x$$

x ga nisbatan hosilani topish

$$36x^{2}-1$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

12x^{3} ni olish uchun 7x^{3} va 5x^{3} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{3}-2-x-3)$$

-5 olish uchun -2 dan 3 ni ayirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{3}-5-x)$$

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

$$3\times 12x^{3-1}-x^{1-1}$$

3 ni 12 marotabaga ko'paytirish.

$$36x^{3-1}-x^{1-1}$$

3 dan 1 ni ayirish.

$$36x^{2}-x^{1-1}$$

1 dan 1 ni ayirish.

$$36x^{2}-x^{0}$$

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

$$36x^{2}-1$$