f(x)=3x/x^2-4 eching

$$f ( x ) = \frac { 3 x } { x ^ { 2 } - 4 }$$

x ga nisbatan hosilani topish

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

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.

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

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

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

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{2}-4\right)\times 3x^{0}-3x^{1}\times 2x^{1}}{\left(x^{2}-4\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{2}\times 3x^{0}-4\times 3x^{0}-3x^{1}\times 2x^{1}}{\left(x^{2}-4\right)^{2}}$$

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

$$\frac{3x^{2}-4\times 3x^{0}-3\times 2x^{1+1}}{\left(x^{2}-4\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{3x^{2}-12x^{0}-6x^{2}}{\left(x^{2}-4\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(3-6\right)x^{2}-12x^{0}}{\left(x^{2}-4\right)^{2}}$$

3 dan 6 ni ayirish.

$$\frac{-3x^{2}-12x^{0}}{\left(x^{2}-4\right)^{2}}$$

3 omili.

$$\frac{3\left(-x^{2}-4x^{0}\right)}{\left(x^{2}-4\right)^{2}}$$

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

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

Baholash

$$\frac{3x}{x^{2}-4}$$