(5x-x^3+2x-1)+(x^3-5x) eching

$$( 5 x - x ^ { 3 } + 2 x - 1 ) + ( x ^ { 3 } - 5 x )$$

Baholash

$$2x-1$$

Yechim qadamlari

7x ni olish uchun 5x va 2x ni birlashtirish.

$$7x-x^{3}-1+x^{3}-5x$$

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

$$7x-1-5x$$

2x ni olish uchun 7x va -5x ni birlashtirish.

$$2x-1$$

x ga nisbatan hosilani topish

$$2$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

7x ni olish uchun 5x va 2x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x-x^{3}-1+x^{3}-5x)$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x-1-5x)$$

2x ni olish uchun 7x va -5x ni birlashtirish.

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

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

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

1 dan 1 ni ayirish.

$$2x^{0}$$

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

$$2\times 1$$

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

$$2$$