v/v+1+3/v-1-6/v^2-1 eching

$$\frac { v } { v + 1 } + \frac { 3 } { v - 1 } - \frac { 6 } { v ^ { 2 } - 1 }$$

Baholash

$$\frac{v+3}{v+1}$$

Qisqa yechim qadamlari

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

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

\frac{v\left(v-1\right)}{\left(v-1\right)\left(v+1\right)} va \frac{3\left(v+1\right)}{\left(v-1\right)\left(v+1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

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

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

v^{2}-v+3v+3 kabi iboralarga o‘xshab birlashtiring.

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

Faktor: v^{2}-1.

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

\frac{v^{2}+2v+3}{\left(v-1\right)\left(v+1\right)} va \frac{6}{\left(v-1\right)\left(v+1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

v^{2}+2v+3-6 kabi iboralarga o‘xshab birlashtiring.

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

\frac{v^{2}+2v-3}{\left(v-1\right)\left(v+1\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala v-1 ni qisqartiring.

$$\frac{v+3}{v+1}$$

v ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

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

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

\frac{v\left(v-1\right)}{\left(v-1\right)\left(v+1\right)} va \frac{3\left(v+1\right)}{\left(v-1\right)\left(v+1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

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

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

v^{2}-v+3v+3 kabi iboralarga o‘xshab birlashtiring.

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

Faktor: v^{2}-1.

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

\frac{v^{2}+2v+3}{\left(v-1\right)\left(v+1\right)} va \frac{6}{\left(v-1\right)\left(v+1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

v^{2}+2v+3-6 kabi iboralarga o‘xshab birlashtiring.

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

\frac{v^{2}+2v-3}{\left(v-1\right)\left(v+1\right)} ichida hali faktorlanmagan ifodalarni faktorlang.

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

Surat va maxrajdagi ikkala v-1 ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{v+3}{v+1})$$

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

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Keraksiz qavslarni olib tashlash.

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

O'xshash hadlarni birlashtirish.

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

1 dan 1 ni va 1 dan 3 ni ayiring.

$$\frac{-2v^{0}}{\left(v^{1}+1\right)^{2}}$$

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

$$\frac{-2v^{0}}{\left(v+1\right)^{2}}$$

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

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