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

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

x ga nisbatan hosilani topish

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

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.

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Arifmetik hisobni amalga oshirish.

$$\frac{4x^{3}-4x^{1}-4x^{3}}{\left(x^{2}-1\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(4-4\right)x^{3}-4x^{1}}{\left(x^{2}-1\right)^{2}}$$

4 dan 4 ni ayirish.

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

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

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

Baholash

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