2(3-5sqrt{x})-5(x-2sqrt{x})= eching

$$2 ( 3 - 5 \sqrt { x } ) - 5 ( x - 2 \sqrt { x } ) =$$

Baholash

$$6-5x$$

Yechim qadamlari

-5 hosil qilish uchun -1 va 5 ni ko'paytirish.

$$2\left(3-5\sqrt{x}\right)-5\left(x-2\sqrt{x}\right)$$

2 ga 3-5\sqrt{x} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6-10\sqrt{x}-5\left(x-2\sqrt{x}\right)$$

-5 ga x-2\sqrt{x} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$6-10\sqrt{x}-5x+10\sqrt{x}$$

0 ni olish uchun -10\sqrt{x} va 10\sqrt{x} ni birlashtirish.

$$6-5x$$

x ga nisbatan hosilani topish

$$-5$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

-5 hosil qilish uchun -1 va 5 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2\left(3-5\sqrt{x}\right)-5\left(x-2\sqrt{x}\right))$$

2 ga 3-5\sqrt{x} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6-10\sqrt{x}-5\left(x-2\sqrt{x}\right))$$

-5 ga x-2\sqrt{x} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6-10\sqrt{x}-5x+10\sqrt{x})$$

0 ni olish uchun -10\sqrt{x} va 10\sqrt{x} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6-5x)$$

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

$$-5x^{1-1}$$

1 dan 1 ni ayirish.

$$-5x^{0}$$

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

$$-5$$