-5z-34+21z^2-45z+83z+z^3-42z^2+5= eching

$$-5z-34+21 { z }^{ 2 } -45z+83z+ { z }^{ 3 } -42 { z }^{ 2 } +5=$$

Baholash

$$z^{3}-21z^{2}+33z-29$$

Yechim qadamlari

-50z ni olish uchun -5z va -45z ni birlashtirish.

$$-50z-34+21z^{2}+83z+z^{3}-42z^{2}+5$$

33z ni olish uchun -50z va 83z ni birlashtirish.

$$33z-34+21z^{2}+z^{3}-42z^{2}+5$$

-21z^{2} ni olish uchun 21z^{2} va -42z^{2} ni birlashtirish.

$$33z-34-21z^{2}+z^{3}+5$$

-29 olish uchun -34 va 5'ni qo'shing.

$$33z-29-21z^{2}+z^{3}$$

z ga nisbatan hosilani topish

$$3\left(z^{2}-14z+11\right)$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

-50z ni olish uchun -5z va -45z ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}z}(-50z-34+21z^{2}+83z+z^{3}-42z^{2}+5)$$

33z ni olish uchun -50z va 83z ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}z}(33z-34+21z^{2}+z^{3}-42z^{2}+5)$$

-21z^{2} ni olish uchun 21z^{2} va -42z^{2} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}z}(33z-34-21z^{2}+z^{3}+5)$$

-29 olish uchun -34 va 5'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}z}(33z-29-21z^{2}+z^{3})$$

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

$$33z^{1-1}+2\left(-21\right)z^{2-1}+3z^{3-1}$$

1 dan 1 ni ayirish.

$$33z^{0}+2\left(-21\right)z^{2-1}+3z^{3-1}$$

2 ni -21 marotabaga ko'paytirish.

$$33z^{0}-42z^{2-1}+3z^{3-1}$$

2 dan 1 ni ayirish.

$$33z^{0}-42z^{1}+3z^{3-1}$$

3 dan 1 ni ayirish.

$$33z^{0}-42z^{1}+3z^{2}$$

Har qanday t sharti uchun t^{1}=t.

$$33z^{0}-42z+3z^{2}$$

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

$$33\times 1-42z+3z^{2}$$

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

$$33-42z+3z^{2}$$