x+2+2/2x-1 eching

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

Baholash

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

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x+2 ni \frac{2x-1}{2x-1} marotabaga ko'paytirish.

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

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

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

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

$$\frac{2x^{2}-x+4x-2+2}{2x-1}$$

2x^{2}-x+4x-2+2 kabi iboralarga o‘xshab birlashtiring.

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

x ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x+2 ni \frac{2x-1}{2x-1} marotabaga ko'paytirish.

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

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{2}-x+4x-2+2}{2x-1})$$

2x^{2}-x+4x-2+2 kabi iboralarga o‘xshab birlashtiring.

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

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

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

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

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

Qisqartirish.

$$\frac{\left(2x^{1}-1\right)\left(4x^{1}+3x^{0}\right)-\left(2x^{2}+3x^{1}\right)\times 2x^{0}}{\left(2x^{1}-1\right)^{2}}$$

2x^{1}-1 ni 4x^{1}+3x^{0} marotabaga ko'paytirish.

$$\frac{2x^{1}\times 4x^{1}+2x^{1}\times 3x^{0}-4x^{1}-3x^{0}-\left(2x^{2}+3x^{1}\right)\times 2x^{0}}{\left(2x^{1}-1\right)^{2}}$$

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

$$\frac{2x^{1}\times 4x^{1}+2x^{1}\times 3x^{0}-4x^{1}-3x^{0}-\left(2x^{2}\times 2x^{0}+3x^{1}\times 2x^{0}\right)}{\left(2x^{1}-1\right)^{2}}$$

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

$$\frac{2\times 4x^{1+1}+2\times 3x^{1}-4x^{1}-3x^{0}-\left(2\times 2x^{2}+3\times 2x^{1}\right)}{\left(2x^{1}-1\right)^{2}}$$

Qisqartirish.

$$\frac{8x^{2}+6x^{1}-4x^{1}-3x^{0}-\left(4x^{2}+6x^{1}\right)}{\left(2x^{1}-1\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{4x^{2}-4x^{1}-3x^{0}}{\left(2x^{1}-1\right)^{2}}$$

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

$$\frac{4x^{2}-4x-3x^{0}}{\left(2x-1\right)^{2}}$$

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

$$\frac{4x^{2}-4x-3}{\left(2x-1\right)^{2}}$$