3x/2x+8 eching

$$\frac { 3 x } { 2 x + 8 }$$

x ga nisbatan hosilani topish

$$\frac{6}{\left(x+4\right)^{2}}$$

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.

$$\frac{\left(2x^{1}+8\right)\frac{\mathrm{d}}{\mathrm{d}x}(3x^{1})-3x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1}+8)}{\left(2x^{1}+8\right)^{2}}$$

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

$$\frac{\left(2x^{1}+8\right)\times 3x^{1-1}-3x^{1}\times 2x^{1-1}}{\left(2x^{1}+8\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(2x^{1}+8\right)\times 3x^{0}-3x^{1}\times 2x^{0}}{\left(2x^{1}+8\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{2x^{1}\times 3x^{0}+8\times 3x^{0}-3x^{1}\times 2x^{0}}{\left(2x^{1}+8\right)^{2}}$$

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

$$\frac{2\times 3x^{1}+8\times 3x^{0}-3\times 2x^{1}}{\left(2x^{1}+8\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{6x^{1}+24x^{0}-6x^{1}}{\left(2x^{1}+8\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(6-6\right)x^{1}+24x^{0}}{\left(2x^{1}+8\right)^{2}}$$

6 dan 6 ni ayirish.

$$\frac{24x^{0}}{\left(2x^{1}+8\right)^{2}}$$

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

$$\frac{24x^{0}}{\left(2x+8\right)^{2}}$$

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

$$\frac{24\times 1}{\left(2x+8\right)^{2}}$$

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

$$\frac{24}{\left(2x+8\right)^{2}}$$

Baholash

$$\frac{3x}{2\left(x+4\right)}$$