1/x+2-1x-2 eching

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

Baholash

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

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. -x-2 ni \frac{x+2}{x+2} marotabaga ko'paytirish.

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

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

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

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

$$\frac{1-x^{2}-2x-2x-4}{x+2}$$

1-x^{2}-2x-2x-4 kabi iboralarga o‘xshab birlashtiring.

$$\frac{-3-x^{2}-4x}{x+2}$$

x ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. -x-2 ni \frac{x+2}{x+2} marotabaga ko'paytirish.

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

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

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1-x^{2}-2x-2x-4}{x+2})$$

1-x^{2}-2x-2x-4 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-3-x^{2}-4x}{x+2})$$

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

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

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

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

Qisqartirish.

$$\frac{\left(x^{1}+2\right)\left(-2x^{1}-4x^{0}\right)-\left(-x^{2}-4x^{1}-3\right)x^{0}}{\left(x^{1}+2\right)^{2}}$$

x^{1}+2 ni -2x^{1}-4x^{0} marotabaga ko'paytirish.

$$\frac{x^{1}\left(-2\right)x^{1}+x^{1}\left(-4\right)x^{0}+2\left(-2\right)x^{1}+2\left(-4\right)x^{0}-\left(-x^{2}-4x^{1}-3\right)x^{0}}{\left(x^{1}+2\right)^{2}}$$

-x^{2}-4x^{1}-3 ni x^{0} marotabaga ko'paytirish.

$$\frac{x^{1}\left(-2\right)x^{1}+x^{1}\left(-4\right)x^{0}+2\left(-2\right)x^{1}+2\left(-4\right)x^{0}-\left(-x^{2}x^{0}-4x^{1}x^{0}-3x^{0}\right)}{\left(x^{1}+2\right)^{2}}$$

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

$$\frac{-2x^{1+1}-4x^{1}+2\left(-2\right)x^{1}+2\left(-4\right)x^{0}-\left(-x^{2}-4x^{1}-3x^{0}\right)}{\left(x^{1}+2\right)^{2}}$$

Qisqartirish.

$$\frac{-2x^{2}-4x^{1}-4x^{1}-8x^{0}-\left(-x^{2}-4x^{1}-3x^{0}\right)}{\left(x^{1}+2\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{-x^{2}-4x^{1}-5x^{0}}{\left(x^{1}+2\right)^{2}}$$

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

$$\frac{-x^{2}-4x-5x^{0}}{\left(x+2\right)^{2}}$$

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

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