x^3/1-x^2 eching

$$\frac { x ^ { 3 } } { 1 - x ^ { 2 } }$$

x ga nisbatan hosilani topish

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

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.

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Arifmetik hisobni amalga oshirish.

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

O'xshash hadlarni birlashtirish.

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

-3 dan -2 ni ayirish.

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

x^{2} omili.

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

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

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

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

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

Baholash

$$\frac{x^{3}}{1-x^{2}}$$