1/x^2-2x+5dx eching

$$\frac { 1 } { x ^ { 2 } - 2 x + 5 } d x$$

Baholash

$$\frac{dx}{x^{2}-2x+5}$$

Yechim qadamlari

\frac{1}{x^{2}-2x+5}d ni yagona kasrga aylantiring.

$$\frac{d}{x^{2}-2x+5}x$$

\frac{d}{x^{2}-2x+5}x ni yagona kasrga aylantiring.

$$\frac{dx}{x^{2}-2x+5}$$

x ga nisbatan hosilani topish

$$\frac{d\left(5-x^{2}\right)}{\left(x^{2}-2x+5\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

\frac{1}{x^{2}-2x+5}d ni yagona kasrga aylantiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{d}{x^{2}-2x+5}x)$$

\frac{d}{x^{2}-2x+5}x ni yagona kasrga aylantiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{dx}{x^{2}-2x+5})$$

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

$$\frac{\left(x^{2}-2x^{1}+5\right)\frac{\mathrm{d}}{\mathrm{d}x}(dx^{1})-dx^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-2x^{1}+5)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

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

$$\frac{\left(x^{2}-2x^{1}+5\right)dx^{1-1}-dx^{1}\left(2x^{2-1}-2x^{1-1}\right)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

Qisqartirish.

$$\frac{\left(x^{2}-2x^{1}+5\right)dx^{0}-dx^{1}\left(2x^{1}-2x^{0}\right)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

x^{2}-2x^{1}+5 ni dx^{0} marotabaga ko'paytirish.

$$\frac{x^{2}dx^{0}-2x^{1}dx^{0}+5dx^{0}-dx^{1}\left(2x^{1}-2x^{0}\right)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

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

$$\frac{x^{2}dx^{0}-2x^{1}dx^{0}+5dx^{0}-\left(dx^{1}\times 2x^{1}+dx^{1}\left(-2\right)x^{0}\right)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

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

$$\frac{dx^{2}-2dx^{1}+5dx^{0}-\left(d\times 2x^{1+1}+d\left(-2\right)x^{1}\right)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

Qisqartirish.

$$\frac{dx^{2}+\left(-2d\right)x^{1}+5dx^{0}-\left(2dx^{2}+\left(-2d\right)x^{1}\right)}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(-d\right)x^{2}+5dx^{0}}{\left(x^{2}-2x^{1}+5\right)^{2}}$$

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

$$\frac{\left(-d\right)x^{2}+5dx^{0}}{\left(x^{2}-2x+5\right)^{2}}$$

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

$$\frac{\left(-d\right)x^{2}+5d\times 1}{\left(x^{2}-2x+5\right)^{2}}$$

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

$$\frac{\left(-d\right)x^{2}+5d}{\left(x^{2}-2x+5\right)^{2}}$$