2r/r^2-1-1/r+1 eching

$$\frac { 2 r } { r ^ { 2 } - 1 } - \frac { 1 } { r + 1 }$$

Baholash

$$\frac{1}{r-1}$$

Qisqa yechim qadamlari

Faktor: r^{2}-1.

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

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

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

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

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

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

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

2r-r+1 kabi iboralarga o‘xshab birlashtiring.

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

Surat va maxrajdagi ikkala r+1 ni qisqartiring.

$$\frac{1}{r-1}$$

r ga nisbatan hosilani topish

$$-\frac{1}{\left(r-1\right)^{2}}$$

Zanjirli qoidadan foydalanish qadamalari

Faktor: r^{2}-1.

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

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

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

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

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

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

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

2r-r+1 kabi iboralarga o‘xshab birlashtiring.

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

Surat va maxrajdagi ikkala r+1 ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}r}(\frac{1}{r-1})$$

Agar F ikki differensial funksiya f\left(u\right) va u=g\left(x\right)'ning yig'indisi bo'lsa, ya'ni agar F\left(x\right)=f\left(g\left(x\right)\right) bo'lsa, F hosilasi f'ning u martalik hosilasi, g'ning x martalik hosilasi ya'ni \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right) bo'ladi.

$$-\left(r^{1}-1\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}r}(r^{1}-1)$$

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

$$-\left(r^{1}-1\right)^{-2}r^{1-1}$$

Qisqartirish.

$$-r^{0}\left(r^{1}-1\right)^{-2}$$

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

$$-r^{0}\left(r-1\right)^{-2}$$

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

$$-\left(r-1\right)^{-2}$$