2x/2+4/2x+12 eching

$$\frac{ 2x }{ 2 } + \frac{ 4 }{ 2x+12 }$$

Baholash

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

Qisqa yechim qadamlari

2 va 2 ni qisqartiring.

$$x+\frac{4}{2x+12}$$

Faktor: 2x+12.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{2\left(x+6\right)}{2\left(x+6\right)} marotabaga ko'paytirish.

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

\frac{x\times 2\left(x+6\right)}{2\left(x+6\right)} va \frac{4}{2\left(x+6\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

x\times 2\left(x+6\right)+4 ichidagi ko‘paytirishlarni bajaring.

$$\frac{2x^{2}+12x+4}{2\left(x+6\right)}$$

\frac{2x^{2}+12x+4}{2\left(x+6\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{2\left(x-\left(\sqrt{7}-3\right)\right)\left(x-\left(-\sqrt{7}-3\right)\right)}{2\left(x+6\right)}$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$\frac{\left(x-\left(\sqrt{7}-3\right)\right)\left(x-\left(-\sqrt{7}-3\right)\right)}{x+6}$$

\sqrt{7}-3 teskarisini topish uchun har birining teskarisini toping.

$$\frac{\left(x-\sqrt{7}-\left(-3\right)\right)\left(x-\left(-\sqrt{7}-3\right)\right)}{x+6}$$

-3 ning teskarisi 3 ga teng.

$$\frac{\left(x-\sqrt{7}+3\right)\left(x-\left(-\sqrt{7}-3\right)\right)}{x+6}$$

-\sqrt{7}-3 teskarisini topish uchun har birining teskarisini toping.

$$\frac{\left(x-\sqrt{7}+3\right)\left(x-\left(-\sqrt{7}\right)-\left(-3\right)\right)}{x+6}$$

-\sqrt{7} ning teskarisi \sqrt{7} ga teng.

$$\frac{\left(x-\sqrt{7}+3\right)\left(x+\sqrt{7}-\left(-3\right)\right)}{x+6}$$

-3 ning teskarisi 3 ga teng.

$$\frac{\left(x-\sqrt{7}+3\right)\left(x+\sqrt{7}+3\right)}{x+6}$$

x-\sqrt{7}+3 ifodaning har bir elementini x+\sqrt{7}+3 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{x^{2}+x\sqrt{7}+3x-\sqrt{7}x-\left(\sqrt{7}\right)^{2}-3\sqrt{7}+3x+3\sqrt{7}+9}{x+6}$$

0 ni olish uchun x\sqrt{7} va -\sqrt{7}x ni birlashtirish.

$$\frac{x^{2}+3x-\left(\sqrt{7}\right)^{2}-3\sqrt{7}+3x+3\sqrt{7}+9}{x+6}$$

\sqrt{7} kvadrati – 7.

$$\frac{x^{2}+3x-7-3\sqrt{7}+3x+3\sqrt{7}+9}{x+6}$$

6x ni olish uchun 3x va 3x ni birlashtirish.

$$\frac{x^{2}+6x-7-3\sqrt{7}+3\sqrt{7}+9}{x+6}$$

0 ni olish uchun -3\sqrt{7} va 3\sqrt{7} ni birlashtirish.

$$\frac{x^{2}+6x-7+9}{x+6}$$

2 olish uchun -7 va 9'ni qo'shing.

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

x ga nisbatan hosilani topish

$$\frac{x^{2}+12x+34}{\left(x+6\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

2 va 2 ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x+\frac{4}{2x+12})$$

Faktor: 2x+12.

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

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x ni \frac{2\left(x+6\right)}{2\left(x+6\right)} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\times 2\left(x+6\right)}{2\left(x+6\right)}+\frac{4}{2\left(x+6\right)})$$

\frac{x\times 2\left(x+6\right)}{2\left(x+6\right)} va \frac{4}{2\left(x+6\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\times 2\left(x+6\right)+4}{2\left(x+6\right)})$$

x\times 2\left(x+6\right)+4 ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{2}+12x+4}{2\left(x+6\right)})$$

\frac{2x^{2}+12x+4}{2\left(x+6\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\left(x-\left(\sqrt{7}-3\right)\right)\left(x-\left(-\sqrt{7}-3\right)\right)}{2\left(x+6\right)})$$

Surat va maxrajdagi ikkala 2 ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x-\left(\sqrt{7}-3\right)\right)\left(x-\left(-\sqrt{7}-3\right)\right)}{x+6})$$

\sqrt{7}-3 teskarisini topish uchun har birining teskarisini toping.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x-\sqrt{7}-\left(-3\right)\right)\left(x-\left(-\sqrt{7}-3\right)\right)}{x+6})$$

-3 ning teskarisi 3 ga teng.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x-\sqrt{7}+3\right)\left(x-\left(-\sqrt{7}-3\right)\right)}{x+6})$$

-\sqrt{7}-3 teskarisini topish uchun har birining teskarisini toping.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x-\sqrt{7}+3\right)\left(x-\left(-\sqrt{7}\right)-\left(-3\right)\right)}{x+6})$$

-\sqrt{7} ning teskarisi \sqrt{7} ga teng.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x-\sqrt{7}+3\right)\left(x+\sqrt{7}-\left(-3\right)\right)}{x+6})$$

-3 ning teskarisi 3 ga teng.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(x-\sqrt{7}+3\right)\left(x+\sqrt{7}+3\right)}{x+6})$$

x-\sqrt{7}+3 ifodaning har bir elementini x+\sqrt{7}+3 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}+x\sqrt{7}+3x-\sqrt{7}x-\left(\sqrt{7}\right)^{2}-3\sqrt{7}+3x+3\sqrt{7}+9}{x+6})$$

0 ni olish uchun x\sqrt{7} va -\sqrt{7}x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}+3x-\left(\sqrt{7}\right)^{2}-3\sqrt{7}+3x+3\sqrt{7}+9}{x+6})$$

\sqrt{7} kvadrati – 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}+3x-7-3\sqrt{7}+3x+3\sqrt{7}+9}{x+6})$$

6x ni olish uchun 3x va 3x ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}+6x-7-3\sqrt{7}+3\sqrt{7}+9}{x+6})$$

0 ni olish uchun -3\sqrt{7} va 3\sqrt{7} ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}+6x-7+9}{x+6})$$

2 olish uchun -7 va 9'ni qo'shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}+6x+2}{x+6})$$

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

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

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

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

Qisqartirish.

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

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

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

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

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

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

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

Qisqartirish.

$$\frac{2x^{2}+6x^{1}+12x^{1}+36x^{0}-\left(x^{2}+6x^{1}+2x^{0}\right)}{\left(x^{1}+6\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{x^{2}+12x^{1}+34x^{0}}{\left(x^{1}+6\right)^{2}}$$

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

$$\frac{x^{2}+12x+34x^{0}}{\left(x+6\right)^{2}}$$

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

$$\frac{x^{2}+12x+34\times 1}{\left(x+6\right)^{2}}$$

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

$$\frac{x^{2}+12x+34}{\left(x+6\right)^{2}}$$