f(x)=2x/1-x^2 eching

$$f ( x ) = \frac { 2 x } { 1 - x ^ { 2 } }$$

x ga nisbatan hosilani topish

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

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.

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Arifmetik hisobni amalga oshirish.

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

O'xshash hadlarni birlashtirish.

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

-2 dan -4 ni ayirish.

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

2 omili.

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

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

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

Baholash

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