6x^3+4+2x^2*15+x^2 eching

$$6 { x }^{ 3 } +4+2 { x }^{ 2 } \times 15+ { x }^{ 2 }$$

Baholash

$$6x^{3}+31x^{2}+4$$

Yechim qadamlari

30 hosil qilish uchun 2 va 15 ni ko'paytirish.

$$6x^{3}+4+30x^{2}+x^{2}$$

31x^{2} ni olish uchun 30x^{2} va x^{2} ni birlashtirish.

$$6x^{3}+4+31x^{2}$$

x ga nisbatan hosilani topish

$$2x\left(9x+31\right)$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

30 hosil qilish uchun 2 va 15 ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{3}+4+30x^{2}+x^{2})$$

31x^{2} ni olish uchun 30x^{2} va x^{2} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(6x^{3}+4+31x^{2})$$

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

$$3\times 6x^{3-1}+2\times 31x^{2-1}$$

3 ni 6 marotabaga ko'paytirish.

$$18x^{3-1}+2\times 31x^{2-1}$$

3 dan 1 ni ayirish.

$$18x^{2}+2\times 31x^{2-1}$$

2 ni 31 marotabaga ko'paytirish.

$$18x^{2}+62x^{2-1}$$

2 dan 1 ni ayirish.

$$18x^{2}+62x^{1}$$

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

$$18x^{2}+62x$$