2q/-3q^2+18q+21 eching

$$\frac { 2 q } { - 3 q ^ { 2 } + 18 q + 21 }$$

q ga nisbatan hosilani topish

$$\frac{2\left(q^{2}+7\right)}{3\left(\left(q-7\right)\left(q+1\right)\right)^{2}}$$

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.

$$\frac{\left(-3q^{2}+18q^{1}+21\right)\frac{\mathrm{d}}{\mathrm{d}q}(2q^{1})-2q^{1}\frac{\mathrm{d}}{\mathrm{d}q}(-3q^{2}+18q^{1}+21)}{\left(-3q^{2}+18q^{1}+21\right)^{2}}$$

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

$$\frac{\left(-3q^{2}+18q^{1}+21\right)\times 2q^{1-1}-2q^{1}\left(2\left(-3\right)q^{2-1}+18q^{1-1}\right)}{\left(-3q^{2}+18q^{1}+21\right)^{2}}$$

Qisqartirish.

$$\frac{\left(-3q^{2}+18q^{1}+21\right)\times 2q^{0}-2q^{1}\left(-6q^{1}+18q^{0}\right)}{\left(-3q^{2}+18q^{1}+21\right)^{2}}$$

-3q^{2}+18q^{1}+21 ni 2q^{0} marotabaga ko'paytirish.

$$\frac{-3q^{2}\times 2q^{0}+18q^{1}\times 2q^{0}+21\times 2q^{0}-2q^{1}\left(-6q^{1}+18q^{0}\right)}{\left(-3q^{2}+18q^{1}+21\right)^{2}}$$

2q^{1} ni -6q^{1}+18q^{0} marotabaga ko'paytirish.

$$\frac{-3q^{2}\times 2q^{0}+18q^{1}\times 2q^{0}+21\times 2q^{0}-\left(2q^{1}\left(-6\right)q^{1}+2q^{1}\times 18q^{0}\right)}{\left(-3q^{2}+18q^{1}+21\right)^{2}}$$

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

$$\frac{-3\times 2q^{2}+18\times 2q^{1}+21\times 2q^{0}-\left(2\left(-6\right)q^{1+1}+2\times 18q^{1}\right)}{\left(-3q^{2}+18q^{1}+21\right)^{2}}$$

Qisqartirish.

$$\frac{-6q^{2}+36q^{1}+42q^{0}-\left(-12q^{2}+36q^{1}\right)}{\left(-3q^{2}+18q^{1}+21\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{6q^{2}+42q^{0}}{\left(-3q^{2}+18q^{1}+21\right)^{2}}$$

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

$$\frac{6q^{2}+42q^{0}}{\left(-3q^{2}+18q+21\right)^{2}}$$

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

$$\frac{6q^{2}+42\times 1}{\left(-3q^{2}+18q+21\right)^{2}}$$

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

$$\frac{6q^{2}+42}{\left(-3q^{2}+18q+21\right)^{2}}$$

Baholash

$$-\frac{2q}{3\left(q-7\right)\left(q+1\right)}$$