d/dxleft(x^2-x/x^3-x^2-x+1right) eching

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

Baholash

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

\frac{x^{2}-x}{x^{3}-x^{2}-x+1} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala x-1 ni qisqartiring.

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

Hisoblang: \left(x-1\right)\left(x+1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 1 kvadratini chiqarish.

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

Har qanday ikki differensial funksiya uchun ikki funksiyaning koeffitsient hosilasi raqamlagichning hosila marotabasi maxraj minusi va barchasi kvadrat maxrajiga bo'lingan.

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Arifmetik hisobni amalga oshirish.

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

O'xshash hadlarni birlashtirish.

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

1 dan 2 ni ayirish.

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

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

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

x ga nisbatan hosilani topish

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