x^2/x+1 eching

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

x ga nisbatan hosilani topish

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

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.

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Arifmetik hisobni amalga oshirish.

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

O'xshash hadlarni birlashtirish.

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

2 dan 1 ni ayirish.

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

x omili.

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

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

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

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

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

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

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

Baholash

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