3x+2+1/3x+2 eching

$$3x+2+ \frac{ 1 }{ 3x+2 }$$

Baholash

$$\frac{9x^{2}+12x+5}{3x+2}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3x+2 ni \frac{3x+2}{3x+2} marotabaga ko'paytirish.

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

\frac{\left(3x+2\right)\left(3x+2\right)}{3x+2} va \frac{1}{3x+2} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

\left(3x+2\right)\left(3x+2\right)+1 ichidagi ko‘paytirishlarni bajaring.

$$\frac{9x^{2}+6x+6x+4+1}{3x+2}$$

9x^{2}+6x+6x+4+1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{9x^{2}+12x+5}{3x+2}$$

x ga nisbatan hosilani topish

$$\frac{9\left(x+1\right)\left(3x+1\right)}{\left(3x+2\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 3x+2 ni \frac{3x+2}{3x+2} marotabaga ko'paytirish.

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

\frac{\left(3x+2\right)\left(3x+2\right)}{3x+2} va \frac{1}{3x+2} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

\left(3x+2\right)\left(3x+2\right)+1 ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9x^{2}+6x+6x+4+1}{3x+2})$$

9x^{2}+6x+6x+4+1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{9x^{2}+12x+5}{3x+2})$$

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

$$\frac{\left(3x^{1}+2\right)\frac{\mathrm{d}}{\mathrm{d}x}(9x^{2}+12x^{1}+5)-\left(9x^{2}+12x^{1}+5\right)\frac{\mathrm{d}}{\mathrm{d}x}(3x^{1}+2)}{\left(3x^{1}+2\right)^{2}}$$

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

$$\frac{\left(3x^{1}+2\right)\left(2\times 9x^{2-1}+12x^{1-1}\right)-\left(9x^{2}+12x^{1}+5\right)\times 3x^{1-1}}{\left(3x^{1}+2\right)^{2}}$$

Qisqartirish.

$$\frac{\left(3x^{1}+2\right)\left(18x^{1}+12x^{0}\right)-\left(9x^{2}+12x^{1}+5\right)\times 3x^{0}}{\left(3x^{1}+2\right)^{2}}$$

3x^{1}+2 ni 18x^{1}+12x^{0} marotabaga ko'paytirish.

$$\frac{3x^{1}\times 18x^{1}+3x^{1}\times 12x^{0}+2\times 18x^{1}+2\times 12x^{0}-\left(9x^{2}+12x^{1}+5\right)\times 3x^{0}}{\left(3x^{1}+2\right)^{2}}$$

9x^{2}+12x^{1}+5 ni 3x^{0} marotabaga ko'paytirish.

$$\frac{3x^{1}\times 18x^{1}+3x^{1}\times 12x^{0}+2\times 18x^{1}+2\times 12x^{0}-\left(9x^{2}\times 3x^{0}+12x^{1}\times 3x^{0}+5\times 3x^{0}\right)}{\left(3x^{1}+2\right)^{2}}$$

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

$$\frac{3\times 18x^{1+1}+3\times 12x^{1}+2\times 18x^{1}+2\times 12x^{0}-\left(9\times 3x^{2}+12\times 3x^{1}+5\times 3x^{0}\right)}{\left(3x^{1}+2\right)^{2}}$$

Qisqartirish.

$$\frac{54x^{2}+36x^{1}+36x^{1}+24x^{0}-\left(27x^{2}+36x^{1}+15x^{0}\right)}{\left(3x^{1}+2\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{27x^{2}+36x^{1}+9x^{0}}{\left(3x^{1}+2\right)^{2}}$$

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

$$\frac{27x^{2}+36x+9x^{0}}{\left(3x+2\right)^{2}}$$

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

$$\frac{27x^{2}+36x+9\times 1}{\left(3x+2\right)^{2}}$$

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

$$\frac{27x^{2}+36x+9}{\left(3x+2\right)^{2}}$$