2r+2r^2+rr+1 eching

$$2 r + 2 r ^ { 2 } + r r + 1$$

Baholash

$$3r^{2}+2r+1$$

Yechim qadamlari

r^{2} hosil qilish uchun r va r ni ko'paytirish.

$$2r+2r^{2}+r^{2}+1$$

3r^{2} ni olish uchun 2r^{2} va r^{2} ni birlashtirish.

$$2r+3r^{2}+1$$

r ga nisbatan hosilani topish

$$6r+2$$

Yig'indi uchun derivativ qoidasidan foydalanish qadamlari

r^{2} hosil qilish uchun r va r ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}r}(2r+2r^{2}+r^{2}+1)$$

3r^{2} ni olish uchun 2r^{2} va r^{2} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}r}(2r+3r^{2}+1)$$

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

$$2r^{1-1}+2\times 3r^{2-1}$$

1 dan 1 ni ayirish.

$$2r^{0}+2\times 3r^{2-1}$$

2 ni 3 marotabaga ko'paytirish.

$$2r^{0}+6r^{2-1}$$

2 dan 1 ni ayirish.

$$2r^{0}+6r^{1}$$

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

$$2r^{0}+6r$$

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

$$2\times 1+6r$$

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

$$2+6r$$