x^-1+1/x-1= eching

$$x ^ { - 1 } + \frac { 1 } { x - 1 } =$$

Baholash

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

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x^{-1} ni \frac{x-1}{x-1} marotabaga ko'paytirish.

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

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

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

x^{-1}\left(x-1\right)+1 ichidagi ko‘paytirishlarni bajaring.

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

1-\frac{1}{x}+1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{2-\frac{1}{x}}{x-1}$$

x ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x^{-1} ni \frac{x-1}{x-1} marotabaga ko'paytirish.

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

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

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

x^{-1}\left(x-1\right)+1 ichidagi ko‘paytirishlarni bajaring.

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

1-\frac{1}{x}+1 kabi iboralarga o‘xshab birlashtiring.

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

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

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Arifmetik hisobni amalga oshirish.

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

Keraksiz qavslarni olib tashlash.

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

O'xshash hadlarni birlashtirish.

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

1 dan -1 ni ayirish.

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

\frac{1}{x^{2}} omili.

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

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

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

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

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