4/2r+5+3/5r-2 eching

$$\frac { 4 } { 2 r + 5 } + \frac { 3 } { 5 r - 2 }$$

Baholash

$$\frac{26r+7}{\left(5r-2\right)\left(2r+5\right)}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2r+5 va 5r-2 ning eng kichik umumiy karralisi \left(5r-2\right)\left(2r+5\right). \frac{4}{2r+5} ni \frac{5r-2}{5r-2} marotabaga ko'paytirish. \frac{3}{5r-2} ni \frac{2r+5}{2r+5} marotabaga ko'paytirish.

$$\frac{4\left(5r-2\right)}{\left(5r-2\right)\left(2r+5\right)}+\frac{3\left(2r+5\right)}{\left(5r-2\right)\left(2r+5\right)}$$

\frac{4\left(5r-2\right)}{\left(5r-2\right)\left(2r+5\right)} va \frac{3\left(2r+5\right)}{\left(5r-2\right)\left(2r+5\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{4\left(5r-2\right)+3\left(2r+5\right)}{\left(5r-2\right)\left(2r+5\right)}$$

4\left(5r-2\right)+3\left(2r+5\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{20r-8+6r+15}{\left(5r-2\right)\left(2r+5\right)}$$

20r-8+6r+15 kabi iboralarga o‘xshab birlashtiring.

$$\frac{26r+7}{\left(5r-2\right)\left(2r+5\right)}$$

\left(5r-2\right)\left(2r+5\right) ni kengaytirish.

$$\frac{26r+7}{10r^{2}+21r-10}$$

r ga nisbatan hosilani topish

$$-\frac{260r^{2}+140r+407}{\left(\left(5r-2\right)\left(2r+5\right)\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2r+5 va 5r-2 ning eng kichik umumiy karralisi \left(5r-2\right)\left(2r+5\right). \frac{4}{2r+5} ni \frac{5r-2}{5r-2} marotabaga ko'paytirish. \frac{3}{5r-2} ni \frac{2r+5}{2r+5} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{4\left(5r-2\right)}{\left(5r-2\right)\left(2r+5\right)}+\frac{3\left(2r+5\right)}{\left(5r-2\right)\left(2r+5\right)})$$

\frac{4\left(5r-2\right)}{\left(5r-2\right)\left(2r+5\right)} va \frac{3\left(2r+5\right)}{\left(5r-2\right)\left(2r+5\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{4\left(5r-2\right)+3\left(2r+5\right)}{\left(5r-2\right)\left(2r+5\right)})$$

4\left(5r-2\right)+3\left(2r+5\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{20r-8+6r+15}{\left(5r-2\right)\left(2r+5\right)})$$

20r-8+6r+15 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{26r+7}{\left(5r-2\right)\left(2r+5\right)})$$

5r-2 ifodaning har bir elementini 2r+5 ifodaning har bir elementiga ko‘paytirish orqali taqsimot qonuni xususiyatlarini qo‘llash mumkin.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{26r+7}{10r^{2}+25r-4r-10})$$

21r ni olish uchun 25r va -4r ni birlashtirish.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{26r+7}{10r^{2}+21r-10})$$

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

$$\frac{\left(10r^{2}+21r^{1}-10\right)\frac{\mathrm{d}}{\mathrm{d}r}(26r^{1}+7)-\left(26r^{1}+7\right)\frac{\mathrm{d}}{\mathrm{d}r}(10r^{2}+21r^{1}-10)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

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

$$\frac{\left(10r^{2}+21r^{1}-10\right)\times 26r^{1-1}-\left(26r^{1}+7\right)\left(2\times 10r^{2-1}+21r^{1-1}\right)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

Qisqartirish.

$$\frac{\left(10r^{2}+21r^{1}-10\right)\times 26r^{0}-\left(26r^{1}+7\right)\left(20r^{1}+21r^{0}\right)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

10r^{2}+21r^{1}-10 ni 26r^{0} marotabaga ko'paytirish.

$$\frac{10r^{2}\times 26r^{0}+21r^{1}\times 26r^{0}-10\times 26r^{0}-\left(26r^{1}+7\right)\left(20r^{1}+21r^{0}\right)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

26r^{1}+7 ni 20r^{1}+21r^{0} marotabaga ko'paytirish.

$$\frac{10r^{2}\times 26r^{0}+21r^{1}\times 26r^{0}-10\times 26r^{0}-\left(26r^{1}\times 20r^{1}+26r^{1}\times 21r^{0}+7\times 20r^{1}+7\times 21r^{0}\right)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

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

$$\frac{10\times 26r^{2}+21\times 26r^{1}-10\times 26r^{0}-\left(26\times 20r^{1+1}+26\times 21r^{1}+7\times 20r^{1}+7\times 21r^{0}\right)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

Qisqartirish.

$$\frac{260r^{2}+546r^{1}-260r^{0}-\left(520r^{2}+546r^{1}+140r^{1}+147r^{0}\right)}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-260r^{2}-140r^{1}-407r^{0}}{\left(10r^{2}+21r^{1}-10\right)^{2}}$$

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

$$\frac{-260r^{2}-140r-407r^{0}}{\left(10r^{2}+21r-10\right)^{2}}$$

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

$$\frac{-260r^{2}-140r-407}{\left(10r^{2}+21r-10\right)^{2}}$$