1x/2x^2-3x+1 eching

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

x ga nisbatan hosilani topish

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

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.

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

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

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

Qisqartirish.

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

2x^{2}-3x^{1}+1 ni x^{0} marotabaga ko'paytirish.

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

x^{1} ni 4x^{1}-3x^{0} marotabaga ko'paytirish.

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

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

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

Qisqartirish.

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

O'xshash hadlarni birlashtirish.

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

Har qanday t sharti uchun t^{1}=t.

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

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

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

Baholash

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