x/2-3x^2 eching

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

x ga nisbatan hosilani topish

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

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.

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Arifmetik hisobni amalga oshirish.

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

O'xshash hadlarni birlashtirish.

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

-3 dan -6 ni ayirish.

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

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

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

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

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

Baholash

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