2/2a+3-1/3-2a eching

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

Baholash

$$\frac{3\left(1-2a\right)}{9-4a^{2}}$$

Qisqa yechim qadamlari

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

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

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

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

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

$$\frac{-4a+6-2a-3}{\left(-2a+3\right)\left(2a+3\right)}$$

-4a+6-2a-3 kabi iboralarga o‘xshab birlashtiring.

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

\left(-2a+3\right)\left(2a+3\right) ni kengaytirish.

$$\frac{-6a+3}{-4a^{2}+9}$$

a ga nisbatan hosilani topish

$$-\frac{6\left(4a^{2}-4a+9\right)}{\left(4a^{2}-9\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

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

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

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{-4a+6-2a-3}{\left(-2a+3\right)\left(2a+3\right)})$$

-4a+6-2a-3 kabi iboralarga o‘xshab birlashtiring.

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

-2a+3 ifodaning har bir elementini 2a+3 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

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

0 ni olish uchun -6a va 6a ni birlashtirish.

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

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

$$\frac{\left(-4a^{2}+9\right)\frac{\mathrm{d}}{\mathrm{d}a}(-6a^{1}+3)-\left(-6a^{1}+3\right)\frac{\mathrm{d}}{\mathrm{d}a}(-4a^{2}+9)}{\left(-4a^{2}+9\right)^{2}}$$

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

$$\frac{\left(-4a^{2}+9\right)\left(-6\right)a^{1-1}-\left(-6a^{1}+3\right)\times 2\left(-4\right)a^{2-1}}{\left(-4a^{2}+9\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(-4a^{2}+9\right)\left(-6\right)a^{0}-\left(-6a^{1}+3\right)\left(-8\right)a^{1}}{\left(-4a^{2}+9\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{-4a^{2}\left(-6\right)a^{0}+9\left(-6\right)a^{0}-\left(-6a^{1}\left(-8\right)a^{1}+3\left(-8\right)a^{1}\right)}{\left(-4a^{2}+9\right)^{2}}$$

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

$$\frac{-4\left(-6\right)a^{2}+9\left(-6\right)a^{0}-\left(-6\left(-8\right)a^{1+1}+3\left(-8\right)a^{1}\right)}{\left(-4a^{2}+9\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{24a^{2}-54a^{0}-\left(48a^{2}-24a^{1}\right)}{\left(-4a^{2}+9\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{24a^{2}-54a^{0}-48a^{2}-\left(-24a^{1}\right)}{\left(-4a^{2}+9\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(24-48\right)a^{2}-54a^{0}-\left(-24a^{1}\right)}{\left(-4a^{2}+9\right)^{2}}$$

24 dan 48 ni ayirish.

$$\frac{-24a^{2}-54a^{0}-\left(-24a^{1}\right)}{\left(-4a^{2}+9\right)^{2}}$$

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

$$\frac{-24a^{2}-54a^{0}-\left(-24a\right)}{\left(-4a^{2}+9\right)^{2}}$$

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

$$\frac{-24a^{2}-54-\left(-24a\right)}{\left(-4a^{2}+9\right)^{2}}$$