(1/x+1-1/1-xdivx^2/1-x^2 eching

$$( \frac{ 1 }{ x+1 } - \frac{ 1 }{ 1-x } \div \frac{ { x }^{ 2 } }{ 1- { x }^{ 2 } }$$

Baholash

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

Qisqa yechim qadamlari

\frac{1}{1-x} ni \frac{x^{2}}{1-x^{2}} ga bo'lish \frac{1}{1-x} ga k'paytirish \frac{x^{2}}{1-x^{2}} ga qaytarish.

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

\frac{1-x^{2}}{\left(1-x\right)x^{2}} ichida hali faktorlanmagan ifodalarni faktorlang.

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

-1+x mislodagi manfiy ishorani chiqarib tashlang.

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

Surat va maxrajdagi ikkala -x+1 ni qisqartiring.

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

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

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

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

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

x^{2}-\left(-\left(-x-1\right)\left(x+1\right)\right) ichidagi ko‘paytirishlarni bajaring.

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

x^{2}-x^{2}-x-x-1 kabi iboralarga o‘xshab birlashtiring.

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

\left(x+1\right)x^{2} ni kengaytirish.

$$\frac{-2x-1}{x^{3}+x^{2}}$$

x ga nisbatan hosilani topish

$$\frac{4x^{2}+5x+2}{\left(x+1\right)^{2}x^{3}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

\frac{1}{1-x} ni \frac{x^{2}}{1-x^{2}} ga bo'lish \frac{1}{1-x} ga k'paytirish \frac{x^{2}}{1-x^{2}} ga qaytarish.

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

\frac{1-x^{2}}{\left(1-x\right)x^{2}} ichida hali faktorlanmagan ifodalarni faktorlang.

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

-1+x mislodagi manfiy ishorani chiqarib tashlang.

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

Surat va maxrajdagi ikkala -x+1 ni qisqartiring.

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

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

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

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

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

x^{2}-\left(-\left(-x-1\right)\left(x+1\right)\right) ichidagi ko‘paytirishlarni bajaring.

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

x^{2}-x^{2}-x-x-1 kabi iboralarga o‘xshab birlashtiring.

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

x+1 ga x^{2} ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

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

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

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

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

Qisqartirish.

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

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

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

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

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

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

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

Qisqartirish.

$$\frac{-2x^{3}-2x^{2}-\left(-6x^{3}-4x^{2}-3x^{2}-2x^{1}\right)}{\left(x^{3}+x^{2}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{4x^{3}+2x^{2}-\left(-3x^{2}\right)-\left(-2x^{1}\right)}{\left(x^{3}+x^{2}\right)^{2}}$$

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

$$\frac{4x^{3}+2x^{2}-\left(-3x^{2}\right)-\left(-2x\right)}{\left(x^{3}+x^{2}\right)^{2}}$$