2x/x^2+x+1 eching

$$\frac{ 2x }{ { x }^{ 2 } +x+1 }$$

x ga nisbatan hosilani topish

$$\frac{2\left(1-x^{2}\right)}{\left(x^{2}+x+1\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Har qanday ikki differensial funksiya uchun ikki funksiyaning koeffitsient hosilasi raqamlagichning hosila marotabasi maxraj minusi va barchasi kvadrat maxrajiga bo'lingan.

$$\frac{\left(x^{2}+x^{1}+1\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1})-2x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+x^{1}+1)}{\left(x^{2}+x^{1}+1\right)^{2}}$$

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

$$\frac{\left(x^{2}+x^{1}+1\right)\times 2x^{1-1}-2x^{1}\left(2x^{2-1}+x^{1-1}\right)}{\left(x^{2}+x^{1}+1\right)^{2}}$$

Qisqartirish.

$$\frac{\left(x^{2}+x^{1}+1\right)\times 2x^{0}-2x^{1}\left(2x^{1}+x^{0}\right)}{\left(x^{2}+x^{1}+1\right)^{2}}$$

x^{2}+x^{1}+1 ni 2x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 2x^{0}+x^{1}\times 2x^{0}+2x^{0}-2x^{1}\left(2x^{1}+x^{0}\right)}{\left(x^{2}+x^{1}+1\right)^{2}}$$

2x^{1} ni 2x^{1}+x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 2x^{0}+x^{1}\times 2x^{0}+2x^{0}-\left(2x^{1}\times 2x^{1}+2x^{1}x^{0}\right)}{\left(x^{2}+x^{1}+1\right)^{2}}$$

Ayni daraja ko'rsatkichlarini ko'paytirish uchun ularning darajalarini qo'shing.

$$\frac{2x^{2}+2x^{1}+2x^{0}-\left(2\times 2x^{1+1}+2x^{1}\right)}{\left(x^{2}+x^{1}+1\right)^{2}}$$

Qisqartirish.

$$\frac{2x^{2}+2x^{1}+2x^{0}-\left(4x^{2}+2x^{1}\right)}{\left(x^{2}+x^{1}+1\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-2x^{2}+2x^{0}}{\left(x^{2}+x^{1}+1\right)^{2}}$$

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

$$\frac{-2x^{2}+2x^{0}}{\left(x^{2}+x+1\right)^{2}}$$

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

$$\frac{-2x^{2}+2\times 1}{\left(x^{2}+x+1\right)^{2}}$$

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

$$\frac{-2x^{2}+2}{\left(x^{2}+x+1\right)^{2}}$$

Baholash

$$\frac{2x}{x^{2}+x+1}$$