2x/1+1{1+frac{x/1-x}}= eching

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

Baholash

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

Qisqa yechim qadamlari

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

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

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

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

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

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

1 ni \frac{1}{1-x} ga bo'lish 1 ga k'paytirish \frac{1}{1-x} ga qaytarish.

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

2 olish uchun 1 va 1'ni qo'shing.

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

x ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

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

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

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

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

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

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

1 ni \frac{1}{1-x} ga bo'lish 1 ga k'paytirish \frac{1}{1-x} ga qaytarish.

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

2 olish uchun 1 va 1'ni qo'shing.

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

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

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Arifmetik hisobni amalga oshirish.

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

O'xshash hadlarni birlashtirish.

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

-2 dan -2 ni ayirish.

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

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

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

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

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

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

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