f(x)=x^2/x^2-4 eching

$$f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } - 4 }$$

x ga nisbatan hosilani topish

$$-\frac{8x}{\left(x^{2}-4\right)^{2}}$$

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.

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Arifmetik hisobni amalga oshirish.

$$\frac{2x^{3}-8x^{1}-2x^{3}}{\left(x^{2}-4\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(2-2\right)x^{3}-8x^{1}}{\left(x^{2}-4\right)^{2}}$$

2 dan 2 ni ayirish.

$$\frac{-8x^{1}}{\left(x^{2}-4\right)^{2}}$$

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

$$\frac{-8x}{\left(x^{2}-4\right)^{2}}$$

Baholash

$$\frac{x^{2}}{x^{2}-4}$$