f(x)=2x/x^2-9 eching

$$f ( x ) = \frac { 2 x } { x ^ { 2 } - 9 }$$

x ga nisbatan hosilani topish

$$-\frac{2\left(x^{2}+9\right)}{\left(x^{2}-9\right)^{2}}$$

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.

$$\frac{\left(x^{2}-9\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1})-2x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-9)}{\left(x^{2}-9\right)^{2}}$$

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

$$\frac{\left(x^{2}-9\right)\times 2x^{1-1}-2x^{1}\times 2x^{2-1}}{\left(x^{2}-9\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{2}-9\right)\times 2x^{0}-2x^{1}\times 2x^{1}}{\left(x^{2}-9\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{2}\times 2x^{0}-9\times 2x^{0}-2x^{1}\times 2x^{1}}{\left(x^{2}-9\right)^{2}}$$

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

$$\frac{2x^{2}-9\times 2x^{0}-2\times 2x^{1+1}}{\left(x^{2}-9\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{2x^{2}-18x^{0}-4x^{2}}{\left(x^{2}-9\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(2-4\right)x^{2}-18x^{0}}{\left(x^{2}-9\right)^{2}}$$

2 dan 4 ni ayirish.

$$\frac{-2x^{2}-18x^{0}}{\left(x^{2}-9\right)^{2}}$$

2 omili.

$$\frac{2\left(-x^{2}-9x^{0}\right)}{\left(x^{2}-9\right)^{2}}$$

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

$$\frac{2\left(-x^{2}-9\right)}{\left(x^{2}-9\right)^{2}}$$

Baholash

$$\frac{2x}{x^{2}-9}$$