2/n-1/n+1 eching

$$\frac { 2 } { n } - \frac { 1 } { n + 1 }$$

Baholash

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

Qisqa yechim qadamlari

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

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

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

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

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

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

2n+2-n kabi iboralarga o‘xshab birlashtiring.

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

n\left(n+1\right) ni kengaytirish.

$$\frac{n+2}{n^{2}+n}$$

n ga nisbatan hosilani topish

$$-\frac{n^{2}+4n+2}{\left(n\left(n+1\right)\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

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

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

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

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

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

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

2n+2-n kabi iboralarga o‘xshab birlashtiring.

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

n ga n+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{n+2}{n^{2}+n})$$

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

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

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

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

Qisqartirish.

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

n^{2}+n^{1} ni n^{0} marotabaga ko'paytirish.

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

n^{1}+2 ni 2n^{1}+n^{0} marotabaga ko'paytirish.

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

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

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

Qisqartirish.

$$\frac{n^{2}+n^{1}-\left(2n^{2}+n^{1}+4n^{1}+2n^{0}\right)}{\left(n^{2}+n^{1}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-n^{2}-4n^{1}-2n^{0}}{\left(n^{2}+n^{1}\right)^{2}}$$

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

$$\frac{-n^{2}-4n-2n^{0}}{\left(n^{2}+n\right)^{2}}$$

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

$$\frac{-n^{2}-4n-2}{\left(n^{2}+n\right)^{2}}$$