1/n-1/n+1 eching

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

Baholash

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

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{1}{n} ni \frac{n+1}{n+1} marotabaga ko'paytirish. \frac{1}{n+1} ni \frac{n}{n} marotabaga ko'paytirish.

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

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

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

n+1-n kabi iboralarga o‘xshab birlashtiring.

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

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

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

n ga nisbatan hosilani topish

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

Zanjirli qoidadan foydalanish qadamalari

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{1}{n} ni \frac{n+1}{n+1} marotabaga ko'paytirish. \frac{1}{n+1} ni \frac{n}{n} marotabaga ko'paytirish.

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

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

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

n+1-n kabi iboralarga o‘xshab birlashtiring.

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

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

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

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.

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

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

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

Qisqartirish.

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

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

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

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

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