(sqrt{x+2}-2)(sqrt{x+2}+2) eching

$$( \sqrt{ x+2 } -2)( \sqrt{ x+2 } +2)$$

Baholash

$$x-2$$

Yechim qadamlari

Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\left(\sqrt{x+2}\right)^{2}-2^{2}$$

2 daraja ko‘rsatkichini \sqrt{x+2} ga hisoblang va x+2 ni qiymatni oling.

$$x+2-2^{2}$$

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

$$x+2-4$$

-2 olish uchun 2 dan 4 ni ayirish.

$$x-2$$

x ga nisbatan hosilani topish

$$1$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

Hisoblang: \left(\sqrt{x+2}-2\right)\left(\sqrt{x+2}+2\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(\sqrt{x+2}\right)^{2}-2^{2})$$

2 daraja ko‘rsatkichini \sqrt{x+2} ga hisoblang va x+2 ni qiymatni oling.

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

2 daraja ko‘rsatkichini 2 ga hisoblang va 4 ni qiymatni oling.

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

-2 olish uchun 2 dan 4 ni ayirish.

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

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

$$x^{1-1}$$

1 dan 1 ni ayirish.

$$x^{0}$$

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

$$1$$