f^3-5f+25-4f^2-12f+9 eching

$${ f }^{ 3 } -5f+25-4 { f }^{ 2 } -12f+9$$

Baholash

$$f^{3}-4f^{2}-17f+34$$

Yechim qadamlari

-17f ni olish uchun -5f va -12f ni birlashtirish.

$$f^{3}-17f+25-4f^{2}+9$$

34 olish uchun 25 va 9'ni qo'shing.

$$f^{3}-17f+34-4f^{2}$$

f ga nisbatan hosilani topish

$$3f^{2}-8f-17$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

-17f ni olish uchun -5f va -12f ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f^{3}-17f+25-4f^{2}+9)$$

34 olish uchun 25 va 9'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f^{3}-17f+34-4f^{2})$$

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

$$3f^{3-1}-17f^{1-1}+2\left(-4\right)f^{2-1}$$

3 dan 1 ni ayirish.

$$3f^{2}-17f^{1-1}+2\left(-4\right)f^{2-1}$$

1 dan 1 ni ayirish.

$$3f^{2}-17f^{0}+2\left(-4\right)f^{2-1}$$

1 ni -17 marotabaga ko'paytirish.

$$3f^{2}-17f^{0}-8f^{2-1}$$

2 dan 1 ni ayirish.

$$3f^{2}-17f^{0}-8f^{1}$$

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

$$3f^{2}-17f^{0}-8f$$

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

$$3f^{2}-17-8f$$