3x/x^2+5x+6 eching

$$\frac { 3 x } { x ^ { 2 } + 5 x + 6 }$$

x ga nisbatan hosilani topish

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

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.

$$\frac{\left(x^{2}+5x^{1}+6\right)\frac{\mathrm{d}}{\mathrm{d}x}(3x^{1})-3x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}+5x^{1}+6)}{\left(x^{2}+5x^{1}+6\right)^{2}}$$

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

$$\frac{\left(x^{2}+5x^{1}+6\right)\times 3x^{1-1}-3x^{1}\left(2x^{2-1}+5x^{1-1}\right)}{\left(x^{2}+5x^{1}+6\right)^{2}}$$

Qisqartirish.

$$\frac{\left(x^{2}+5x^{1}+6\right)\times 3x^{0}-3x^{1}\left(2x^{1}+5x^{0}\right)}{\left(x^{2}+5x^{1}+6\right)^{2}}$$

x^{2}+5x^{1}+6 ni 3x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 3x^{0}+5x^{1}\times 3x^{0}+6\times 3x^{0}-3x^{1}\left(2x^{1}+5x^{0}\right)}{\left(x^{2}+5x^{1}+6\right)^{2}}$$

3x^{1} ni 2x^{1}+5x^{0} marotabaga ko'paytirish.

$$\frac{x^{2}\times 3x^{0}+5x^{1}\times 3x^{0}+6\times 3x^{0}-\left(3x^{1}\times 2x^{1}+3x^{1}\times 5x^{0}\right)}{\left(x^{2}+5x^{1}+6\right)^{2}}$$

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

$$\frac{3x^{2}+5\times 3x^{1}+6\times 3x^{0}-\left(3\times 2x^{1+1}+3\times 5x^{1}\right)}{\left(x^{2}+5x^{1}+6\right)^{2}}$$

Qisqartirish.

$$\frac{3x^{2}+15x^{1}+18x^{0}-\left(6x^{2}+15x^{1}\right)}{\left(x^{2}+5x^{1}+6\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-3x^{2}+18x^{0}}{\left(x^{2}+5x^{1}+6\right)^{2}}$$

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

$$\frac{-3x^{2}+18x^{0}}{\left(x^{2}+5x+6\right)^{2}}$$

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

$$\frac{-3x^{2}+18\times 1}{\left(x^{2}+5x+6\right)^{2}}$$

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

$$\frac{-3x^{2}+18}{\left(x^{2}+5x+6\right)^{2}}$$

Baholash

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