h(x)=-x/3x^2-9 eching

$$h ( x ) = \frac { - x } { 3 x ^ { 2 } - 9 }$$

x ga nisbatan hosilani topish

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

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.

$$\frac{\left(3x^{2}-9\right)\frac{\mathrm{d}}{\mathrm{d}x}(-x^{1})-\left(-x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}-9)\right)}{\left(3x^{2}-9\right)^{2}}$$

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

$$\frac{\left(3x^{2}-9\right)\left(-1\right)x^{1-1}-\left(-x^{1}\times 2\times 3x^{2-1}\right)}{\left(3x^{2}-9\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(3x^{2}-9\right)\left(-1\right)x^{0}-\left(-x^{1}\times 6x^{1}\right)}{\left(3x^{2}-9\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{3x^{2}\left(-1\right)x^{0}-9\left(-1\right)x^{0}-\left(-x^{1}\times 6x^{1}\right)}{\left(3x^{2}-9\right)^{2}}$$

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

$$\frac{3\left(-1\right)x^{2}-9\left(-1\right)x^{0}-\left(-6x^{1+1}\right)}{\left(3x^{2}-9\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{-3x^{2}+9x^{0}-\left(-6x^{2}\right)}{\left(3x^{2}-9\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(-3-\left(-6\right)\right)x^{2}+9x^{0}}{\left(3x^{2}-9\right)^{2}}$$

-3 dan -6 ni ayirish.

$$\frac{3x^{2}+9x^{0}}{\left(3x^{2}-9\right)^{2}}$$

3 omili.

$$\frac{3\left(x^{2}+3x^{0}\right)}{\left(3x^{2}-9\right)^{2}}$$

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

$$\frac{3\left(x^{2}+3\times 1\right)}{\left(3x^{2}-9\right)^{2}}$$

Har qanday t sharti uchun t\times 1=t va 1t=t.

$$\frac{3\left(x^{2}+3\right)}{\left(3x^{2}-9\right)^{2}}$$

Baholash

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