2x/x^4-1 eching

$$\frac { 2 x } { x ^ { 4 } - 1 }$$

x ga nisbatan hosilani topish

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

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.

$$\frac{\left(x^{4}-1\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1})-2x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}-1)}{\left(x^{4}-1\right)^{2}}$$

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

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

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{4}-1\right)\times 2x^{0}-2x^{1}\times 4x^{3}}{\left(x^{4}-1\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{4}\times 2x^{0}-2x^{0}-2x^{1}\times 4x^{3}}{\left(x^{4}-1\right)^{2}}$$

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

$$\frac{2x^{4}-2x^{0}-2\times 4x^{1+3}}{\left(x^{4}-1\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{2x^{4}-2x^{0}-8x^{4}}{\left(x^{4}-1\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(2-8\right)x^{4}-2x^{0}}{\left(x^{4}-1\right)^{2}}$$

2 dan 8 ni ayirish.

$$\frac{-6x^{4}-2x^{0}}{\left(x^{4}-1\right)^{2}}$$

2 omili.

$$\frac{2\left(-3x^{4}-x^{0}\right)}{\left(x^{4}-1\right)^{2}}$$

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

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

Baholash

$$\frac{2x}{x^{4}-1}$$