1/x+2/frac{6{x}} eching

$$\frac { \frac { 1 } { x + 2 } } { \frac { 6 } { x } }$$

Baholash

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

Qisqa yechim qadamlari

\frac{1}{x+2} ni \frac{6}{x} ga bo'lish \frac{1}{x+2} ga k'paytirish \frac{6}{x} ga qaytarish.

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

x+2 ga 6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{x}{6x+12}$$

x ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

\frac{1}{x+2} ni \frac{6}{x} ga bo'lish \frac{1}{x+2} ga k'paytirish \frac{6}{x} ga qaytarish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{\left(x+2\right)\times 6})$$

x+2 ga 6 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{6x+12})$$

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

$$\frac{\left(6x^{1}+12\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1})-x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(6x^{1}+12)}{\left(6x^{1}+12\right)^{2}}$$

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

$$\frac{\left(6x^{1}+12\right)x^{1-1}-x^{1}\times 6x^{1-1}}{\left(6x^{1}+12\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(6x^{1}+12\right)x^{0}-x^{1}\times 6x^{0}}{\left(6x^{1}+12\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{6x^{1}x^{0}+12x^{0}-x^{1}\times 6x^{0}}{\left(6x^{1}+12\right)^{2}}$$

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

$$\frac{6x^{1}+12x^{0}-6x^{1}}{\left(6x^{1}+12\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(6-6\right)x^{1}+12x^{0}}{\left(6x^{1}+12\right)^{2}}$$

6 dan 6 ni ayirish.

$$\frac{12x^{0}}{\left(6x^{1}+12\right)^{2}}$$

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

$$\frac{12x^{0}}{\left(6x+12\right)^{2}}$$

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

$$\frac{12\times 1}{\left(6x+12\right)^{2}}$$

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

$$\frac{12}{\left(6x+12\right)^{2}}$$