x/x^2-100+2/10-x eching

$$\frac { x } { x ^ { 2 } - 100 } + \frac { 2 } { 10 - x }$$

Baholash

$$\frac{x+20}{100-x^{2}}$$

Qisqa yechim qadamlari

Faktor: x^{2}-100.

$$\frac{x}{\left(x-10\right)\left(x+10\right)}+\frac{2}{10-x}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x-10\right)\left(x+10\right) va 10-x ning eng kichik umumiy karralisi \left(x-10\right)\left(x+10\right). \frac{2}{10-x} ni \frac{-\left(x+10\right)}{-\left(x+10\right)} marotabaga ko'paytirish.

$$\frac{x}{\left(x-10\right)\left(x+10\right)}+\frac{2\left(-1\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)}$$

\frac{x}{\left(x-10\right)\left(x+10\right)} va \frac{2\left(-1\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{x+2\left(-1\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)}$$

x+2\left(-1\right)\left(x+10\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{x-2x-20}{\left(x-10\right)\left(x+10\right)}$$

x-2x-20 kabi iboralarga o‘xshab birlashtiring.

$$\frac{-x-20}{\left(x-10\right)\left(x+10\right)}$$

\left(x-10\right)\left(x+10\right) ni kengaytirish.

$$\frac{-x-20}{x^{2}-100}$$

x ga nisbatan hosilani topish

$$\frac{x^{2}+40x+100}{\left(100-x^{2}\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Faktor: x^{2}-100.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{\left(x-10\right)\left(x+10\right)}+\frac{2}{10-x})$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. \left(x-10\right)\left(x+10\right) va 10-x ning eng kichik umumiy karralisi \left(x-10\right)\left(x+10\right). \frac{2}{10-x} ni \frac{-\left(x+10\right)}{-\left(x+10\right)} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{\left(x-10\right)\left(x+10\right)}+\frac{2\left(-1\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)})$$

\frac{x}{\left(x-10\right)\left(x+10\right)} va \frac{2\left(-1\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x+2\left(-1\right)\left(x+10\right)}{\left(x-10\right)\left(x+10\right)})$$

x+2\left(-1\right)\left(x+10\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x-2x-20}{\left(x-10\right)\left(x+10\right)})$$

x-2x-20 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x-20}{\left(x-10\right)\left(x+10\right)})$$

Hisoblang: \left(x-10\right)\left(x+10\right). Ko‘paytirish qoida yordamida turli kvadratlarga aylantirilishi mumkin: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. 10 kvadratini chiqarish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-x-20}{x^{2}-100})$$

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

$$\frac{\left(x^{2}-100\right)\frac{\mathrm{d}}{\mathrm{d}x}(-x^{1}-20)-\left(-x^{1}-20\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}-100)}{\left(x^{2}-100\right)^{2}}$$

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

$$\frac{\left(x^{2}-100\right)\left(-1\right)x^{1-1}-\left(-x^{1}-20\right)\times 2x^{2-1}}{\left(x^{2}-100\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{2}-100\right)\left(-1\right)x^{0}-\left(-x^{1}-20\right)\times 2x^{1}}{\left(x^{2}-100\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{2}\left(-1\right)x^{0}-100\left(-1\right)x^{0}-\left(-x^{1}\times 2x^{1}-20\times 2x^{1}\right)}{\left(x^{2}-100\right)^{2}}$$

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

$$\frac{-x^{2}-100\left(-1\right)x^{0}-\left(-2x^{1+1}-20\times 2x^{1}\right)}{\left(x^{2}-100\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{-x^{2}+100x^{0}-\left(-2x^{2}-40x^{1}\right)}{\left(x^{2}-100\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{-x^{2}+100x^{0}-\left(-2x^{2}\right)-\left(-40x^{1}\right)}{\left(x^{2}-100\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(-1-\left(-2\right)\right)x^{2}+100x^{0}-\left(-40x^{1}\right)}{\left(x^{2}-100\right)^{2}}$$

-1 dan -2 ni ayirish.

$$\frac{x^{2}+100x^{0}-\left(-40x^{1}\right)}{\left(x^{2}-100\right)^{2}}$$

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

$$\frac{x^{2}+100x^{0}-\left(-40x\right)}{\left(x^{2}-100\right)^{2}}$$

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

$$\frac{x^{2}+100\times 1-\left(-40x\right)}{\left(x^{2}-100\right)^{2}}$$

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

$$\frac{x^{2}+100-\left(-40x\right)}{\left(x^{2}-100\right)^{2}}$$