1/x^2-2x-1/x eching

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

Baholash

$$\frac{3-x}{x\left(x-2\right)}$$

Qisqa yechim qadamlari

Faktor: x^{2}-2x.

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

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

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

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

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

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

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

1-x+2 kabi iboralarga o‘xshab birlashtiring.

$$\frac{3-x}{x\left(x-2\right)}$$

x\left(x-2\right) ni kengaytirish.

$$\frac{3-x}{x^{2}-2x}$$

x ga nisbatan hosilani topish

$$\frac{x^{2}-6x+6}{\left(x\left(x-2\right)\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Faktor: x^{2}-2x.

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

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

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

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

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

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

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

1-x+2 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3-x}{x\left(x-2\right)})$$

x ga x-2 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3-x}{x^{2}-2x})$$

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

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

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

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

Qisqartirish.

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

x^{2}-2x^{1} ni -x^{0} marotabaga ko'paytirish.

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

-x^{1}+3 ni 2x^{1}-2x^{0} marotabaga ko'paytirish.

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

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

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

Qisqartirish.

$$\frac{-x^{2}+2x^{1}-\left(-2x^{2}+2x^{1}+6x^{1}-6x^{0}\right)}{\left(x^{2}-2x^{1}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{x^{2}-6x^{1}+6x^{0}}{\left(x^{2}-2x^{1}\right)^{2}}$$

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

$$\frac{x^{2}-6x+6x^{0}}{\left(x^{2}-2x\right)^{2}}$$

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

$$\frac{x^{2}-6x+6\times 1}{\left(x^{2}-2x\right)^{2}}$$

Har qanday t sharti uchun t\times 1=t va 1t=t.

$$\frac{x^{2}-6x+6}{\left(x^{2}-2x\right)^{2}}$$