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

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

Baholash

$$\frac{x+7}{\left(2x-1\right)\left(x+2\right)}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2x-1 va x+2 ning eng kichik umumiy karralisi \left(2x-1\right)\left(x+2\right). \frac{3}{2x-1} ni \frac{x+2}{x+2} marotabaga ko'paytirish. \frac{1}{x+2} ni \frac{2x-1}{2x-1} marotabaga ko'paytirish.

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

\frac{3\left(x+2\right)}{\left(2x-1\right)\left(x+2\right)} va \frac{2x-1}{\left(2x-1\right)\left(x+2\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

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

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

3x+6-2x+1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{x+7}{\left(2x-1\right)\left(x+2\right)}$$

\left(2x-1\right)\left(x+2\right) ni kengaytirish.

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

x ga nisbatan hosilani topish

$$-\frac{2x^{2}+28x+23}{4x^{4}+12x^{3}+x^{2}-12x+4}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2x-1 va x+2 ning eng kichik umumiy karralisi \left(2x-1\right)\left(x+2\right). \frac{3}{2x-1} ni \frac{x+2}{x+2} marotabaga ko'paytirish. \frac{1}{x+2} ni \frac{2x-1}{2x-1} marotabaga ko'paytirish.

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

\frac{3\left(x+2\right)}{\left(2x-1\right)\left(x+2\right)} va \frac{2x-1}{\left(2x-1\right)\left(x+2\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x+6-2x+1}{\left(2x-1\right)\left(x+2\right)})$$

3x+6-2x+1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+7}{\left(2x-1\right)\left(x+2\right)})$$

2x-1 ifodaning har bir elementini x+2 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+7}{2x^{2}+4x-x-2})$$

3x ni olish uchun 4x va -x ni birlashtirish.

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

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

$$\frac{\left(2x^{2}+3x^{1}-2\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}+7)-\left(x^{1}+7\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}+3x^{1}-2)}{\left(2x^{2}+3x^{1}-2\right)^{2}}$$

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

$$\frac{\left(2x^{2}+3x^{1}-2\right)x^{1-1}-\left(x^{1}+7\right)\left(2\times 2x^{2-1}+3x^{1-1}\right)}{\left(2x^{2}+3x^{1}-2\right)^{2}}$$

Qisqartirish.

$$\frac{\left(2x^{2}+3x^{1}-2\right)x^{0}-\left(x^{1}+7\right)\left(4x^{1}+3x^{0}\right)}{\left(2x^{2}+3x^{1}-2\right)^{2}}$$

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

$$\frac{2x^{2}x^{0}+3x^{1}x^{0}-2x^{0}-\left(x^{1}+7\right)\left(4x^{1}+3x^{0}\right)}{\left(2x^{2}+3x^{1}-2\right)^{2}}$$

x^{1}+7 ni 4x^{1}+3x^{0} marotabaga ko'paytirish.

$$\frac{2x^{2}x^{0}+3x^{1}x^{0}-2x^{0}-\left(x^{1}\times 4x^{1}+x^{1}\times 3x^{0}+7\times 4x^{1}+7\times 3x^{0}\right)}{\left(2x^{2}+3x^{1}-2\right)^{2}}$$

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

$$\frac{2x^{2}+3x^{1}-2x^{0}-\left(4x^{1+1}+3x^{1}+7\times 4x^{1}+7\times 3x^{0}\right)}{\left(2x^{2}+3x^{1}-2\right)^{2}}$$

Qisqartirish.

$$\frac{2x^{2}+3x^{1}-2x^{0}-\left(4x^{2}+3x^{1}+28x^{1}+21x^{0}\right)}{\left(2x^{2}+3x^{1}-2\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-2x^{2}-28x^{1}-23x^{0}}{\left(2x^{2}+3x^{1}-2\right)^{2}}$$

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

$$\frac{-2x^{2}-28x-23x^{0}}{\left(2x^{2}+3x-2\right)^{2}}$$

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

$$\frac{-2x^{2}-28x-23}{\left(2x^{2}+3x-2\right)^{2}}$$