1/-x+2/1+x eching

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

Baholash

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

Qisqa yechim qadamlari

Faktor: -x.

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

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

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

\frac{-\left(x+1\right)}{x\left(x+1\right)} va \frac{2x}{x\left(x+1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

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

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

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

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

x\left(x+1\right) ni kengaytirish.

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

x ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Faktor: -x.

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

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

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

\frac{-\left(x+1\right)}{x\left(x+1\right)} va \frac{2x}{x\left(x+1\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

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

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

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

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

x ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

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

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

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

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

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

Qisqartirish.

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

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

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

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

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

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

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

Qisqartirish.

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

O'xshash hadlarni birlashtirish.

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

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

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

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

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