1/x+21/2-x eching

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

Baholash

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

Qisqa yechim qadamlari

2\times \frac{1}{2-x} ni yagona kasrga aylantiring.

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

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

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

\frac{-x+2}{x\left(-x+2\right)} va \frac{2x}{x\left(-x+2\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

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

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

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

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

x ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

2\times \frac{1}{2-x} ni yagona kasrga aylantiring.

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

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

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

\frac{-x+2}{x\left(-x+2\right)} va \frac{2x}{x\left(-x+2\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

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

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

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

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

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

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

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

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

Qisqartirish.

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

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

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

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

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

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

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

Qisqartirish.

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

O'xshash hadlarni birlashtirish.

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

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

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

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

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