-x/x^2+1 eching

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

x ga nisbatan hosilani topish

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

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.

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Arifmetik hisobni amalga oshirish.

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

O'xshash hadlarni birlashtirish.

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

-1 dan -2 ni ayirish.

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

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

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

Baholash

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