1/x+3-x+3 eching

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

Baholash

$$\frac{10-x^{2}}{x+3}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. -x+3 ni \frac{x+3}{x+3} marotabaga ko'paytirish.

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

\frac{1}{x+3} va \frac{\left(-x+3\right)\left(x+3\right)}{x+3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

1+\left(-x+3\right)\left(x+3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{1-x^{2}-3x+3x+9}{x+3}$$

1-x^{2}-3x+3x+9 kabi iboralarga o‘xshab birlashtiring.

$$\frac{10-x^{2}}{x+3}$$

x ga nisbatan hosilani topish

$$-\frac{x^{2}+6x+10}{\left(x+3\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. -x+3 ni \frac{x+3}{x+3} marotabaga ko'paytirish.

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

\frac{1}{x+3} va \frac{\left(-x+3\right)\left(x+3\right)}{x+3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

1+\left(-x+3\right)\left(x+3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1-x^{2}-3x+3x+9}{x+3})$$

1-x^{2}-3x+3x+9 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10-x^{2}}{x+3})$$

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

$$\frac{\left(x^{1}+3\right)\frac{\mathrm{d}}{\mathrm{d}x}(-x^{2}+10)-\left(-x^{2}+10\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}+3)}{\left(x^{1}+3\right)^{2}}$$

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

$$\frac{\left(x^{1}+3\right)\times 2\left(-1\right)x^{2-1}-\left(-x^{2}+10\right)x^{1-1}}{\left(x^{1}+3\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{1}+3\right)\left(-2\right)x^{1}-\left(-x^{2}+10\right)x^{0}}{\left(x^{1}+3\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{1}\left(-2\right)x^{1}+3\left(-2\right)x^{1}-\left(-x^{2}x^{0}+10x^{0}\right)}{\left(x^{1}+3\right)^{2}}$$

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

$$\frac{-2x^{1+1}+3\left(-2\right)x^{1}-\left(-x^{2}+10x^{0}\right)}{\left(x^{1}+3\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{-2x^{2}-6x^{1}-\left(-x^{2}+10x^{0}\right)}{\left(x^{1}+3\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{-2x^{2}-6x^{1}-\left(-x^{2}\right)-10x^{0}}{\left(x^{1}+3\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(-2-\left(-1\right)\right)x^{2}-6x^{1}-10x^{0}}{\left(x^{1}+3\right)^{2}}$$

-2 dan -1 ni ayirish.

$$\frac{-x^{2}-6x^{1}-10x^{0}}{\left(x^{1}+3\right)^{2}}$$

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

$$\frac{-x^{2}-6x-10x^{0}}{\left(x+3\right)^{2}}$$

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

$$\frac{-x^{2}-6x-10\times 1}{\left(x+3\right)^{2}}$$

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

$$\frac{-x^{2}-6x-10}{\left(x+3\right)^{2}}$$