dx/x^2+5x+6 eching

$$\frac { d x } { x ^ { 2 } + 5 x + 6 }$$

x ga nisbatan hosilani topish

$$\frac{d\left(6-x^{2}\right)}{\left(\left(x+2\right)\left(x+3\right)\right)^{2}}$$

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.

$$\frac{\left(x^{2}+5x^{1}+6\right)\frac{\mathrm{d}}{\mathrm{d}x}(dx^{1})-dx^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+5x^{1}+6)}{\left(x^{2}+5x^{1}+6\right)^{2}}$$

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

$$\frac{\left(x^{2}+5x^{1}+6\right)dx^{1-1}-dx^{1}\left(2x^{2-1}+5x^{1-1}\right)}{\left(x^{2}+5x^{1}+6\right)^{2}}$$

Qisqartirish.

$$\frac{\left(x^{2}+5x^{1}+6\right)dx^{0}-dx^{1}\left(2x^{1}+5x^{0}\right)}{\left(x^{2}+5x^{1}+6\right)^{2}}$$

x^{2}+5x^{1}+6 ni dx^{0} marotabaga ko'paytirish.

$$\frac{x^{2}dx^{0}+5x^{1}dx^{0}+6dx^{0}-dx^{1}\left(2x^{1}+5x^{0}\right)}{\left(x^{2}+5x^{1}+6\right)^{2}}$$

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

$$\frac{x^{2}dx^{0}+5x^{1}dx^{0}+6dx^{0}-\left(dx^{1}\times 2x^{1}+dx^{1}\times 5x^{0}\right)}{\left(x^{2}+5x^{1}+6\right)^{2}}$$

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

$$\frac{dx^{2}+5dx^{1}+6dx^{0}-\left(d\times 2x^{1+1}+d\times 5x^{1}\right)}{\left(x^{2}+5x^{1}+6\right)^{2}}$$

Qisqartirish.

$$\frac{dx^{2}+5dx^{1}+6dx^{0}-\left(2dx^{2}+5dx^{1}\right)}{\left(x^{2}+5x^{1}+6\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(-d\right)x^{2}+6dx^{0}}{\left(x^{2}+5x^{1}+6\right)^{2}}$$

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

$$\frac{\left(-d\right)x^{2}+6dx^{0}}{\left(x^{2}+5x+6\right)^{2}}$$

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

$$\frac{\left(-d\right)x^{2}+6d\times 1}{\left(x^{2}+5x+6\right)^{2}}$$

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

$$\frac{\left(-d\right)x^{2}+6d}{\left(x^{2}+5x+6\right)^{2}}$$

Baholash

$$\frac{dx}{\left(x+2\right)\left(x+3\right)}$$