5/x+1+6/x-1 eching

$$\frac{ 5 }{ x+1 } + \frac{ 6 }{ x-1 }$$

Baholash

$$\frac{11x+1}{x^{2}-1}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x+1 va x-1 ning eng kichik umumiy karralisi \left(x-1\right)\left(x+1\right). \frac{5}{x+1} ni \frac{x-1}{x-1} marotabaga ko'paytirish. \frac{6}{x-1} ni \frac{x+1}{x+1} marotabaga ko'paytirish.

$$\frac{5\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}+\frac{6\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}$$

\frac{5\left(x-1\right)}{\left(x-1\right)\left(x+1\right)} va \frac{6\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{5\left(x-1\right)+6\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}$$

5\left(x-1\right)+6\left(x+1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{5x-5+6x+6}{\left(x-1\right)\left(x+1\right)}$$

5x-5+6x+6 kabi iboralarga o‘xshab birlashtiring.

$$\frac{11x+1}{\left(x-1\right)\left(x+1\right)}$$

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

$$\frac{11x+1}{x^{2}-1}$$

x ga nisbatan hosilani topish

$$-\frac{11x^{2}+2x+11}{\left(x^{2}-1\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x+1 va x-1 ning eng kichik umumiy karralisi \left(x-1\right)\left(x+1\right). \frac{5}{x+1} ni \frac{x-1}{x-1} marotabaga ko'paytirish. \frac{6}{x-1} ni \frac{x+1}{x+1} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}+\frac{6\left(x+1\right)}{\left(x-1\right)\left(x+1\right)})$$

\frac{5\left(x-1\right)}{\left(x-1\right)\left(x+1\right)} va \frac{6\left(x+1\right)}{\left(x-1\right)\left(x+1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\left(x-1\right)+6\left(x+1\right)}{\left(x-1\right)\left(x+1\right)})$$

5\left(x-1\right)+6\left(x+1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x-5+6x+6}{\left(x-1\right)\left(x+1\right)})$$

5x-5+6x+6 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x+1}{\left(x-1\right)\left(x+1\right)})$$

Hisoblang: \left(x-1\right)\left(x+1\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x+1}{x^{2}-1^{2}})$$

2 daraja ko‘rsatkichini 1 ga hisoblang va 1 ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11x+1}{x^{2}-1})$$

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

$$\frac{\left(x^{2}-1\right)\frac{\mathrm{d}}{\mathrm{d}x}(11x^{1}+1)-\left(11x^{1}+1\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-1)}{\left(x^{2}-1\right)^{2}}$$

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

$$\frac{\left(x^{2}-1\right)\times 11x^{1-1}-\left(11x^{1}+1\right)\times 2x^{2-1}}{\left(x^{2}-1\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{2}-1\right)\times 11x^{0}-\left(11x^{1}+1\right)\times 2x^{1}}{\left(x^{2}-1\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{2}\times 11x^{0}-11x^{0}-\left(11x^{1}\times 2x^{1}+2x^{1}\right)}{\left(x^{2}-1\right)^{2}}$$

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

$$\frac{11x^{2}-11x^{0}-\left(11\times 2x^{1+1}+2x^{1}\right)}{\left(x^{2}-1\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{11x^{2}-11x^{0}-\left(22x^{2}+2x^{1}\right)}{\left(x^{2}-1\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{11x^{2}-11x^{0}-22x^{2}-2x^{1}}{\left(x^{2}-1\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(11-22\right)x^{2}-11x^{0}-2x^{1}}{\left(x^{2}-1\right)^{2}}$$

11 dan 22 ni ayirish.

$$\frac{-11x^{2}-11x^{0}-2x^{1}}{\left(x^{2}-1\right)^{2}}$$

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

$$\frac{-11x^{2}-11x^{0}-2x}{\left(x^{2}-1\right)^{2}}$$

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

$$\frac{-11x^{2}-11-2x}{\left(x^{2}-1\right)^{2}}$$