(sqrt{3x+1}-2)(sqrt{3x+1}+2) eching

$$( \sqrt { 3 x + 1 } - 2 ) ( \sqrt { 3 x + 1 } + 2 )$$

Baholash

$$3\left(x-1\right)$$

Yechim qadamlari

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

$$\left(\sqrt{3x+1}\right)^{2}-2^{2}$$

2 daraja ko‘rsatkichini \sqrt{3x+1} ga hisoblang va 3x+1 ni qiymatni oling.

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

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

$$3x+1-4$$

-3 olish uchun 1 dan 4 ni ayirish.

$$3x-3$$

x ga nisbatan hosilani topish

$$3$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

Hisoblang: \left(\sqrt{3x+1}-2\right)\left(\sqrt{3x+1}+2\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

2 daraja ko‘rsatkichini \sqrt{3x+1} ga hisoblang va 3x+1 ni qiymatni oling.

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x+1-4)$$

-3 olish uchun 1 dan 4 ni ayirish.

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

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

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

1 dan 1 ni ayirish.

$$3x^{0}$$

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

$$3\times 1$$

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

$$3$$