5/x+3+3 eching

$$\frac { 5 } { x + 3 } + 3$$

Baholash

$$\frac{3x+14}{x+3}$$

Qisqa yechim qadamlari

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

$$\frac{5}{x+3}+\frac{3\left(x+3\right)}{x+3}$$

\frac{5}{x+3} va \frac{3\left(x+3\right)}{x+3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{5+3\left(x+3\right)}{x+3}$$

5+3\left(x+3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{5+3x+9}{x+3}$$

5+3x+9 kabi iboralarga o‘xshab birlashtiring.

$$\frac{14+3x}{x+3}$$

x ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{x+3}+\frac{3\left(x+3\right)}{x+3})$$

\frac{5}{x+3} va \frac{3\left(x+3\right)}{x+3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5+3\left(x+3\right)}{x+3})$$

5+3\left(x+3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5+3x+9}{x+3})$$

5+3x+9 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{14+3x}{x+3})$$

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

$$\frac{\left(x^{1}+3\right)\frac{\mathrm{d}}{\mathrm{d}x}(3x^{1}+14)-\left(3x^{1}+14\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}+3)}{\left(x^{1}+3\right)^{2}}$$

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

$$\frac{\left(x^{1}+3\right)\times 3x^{1-1}-\left(3x^{1}+14\right)x^{1-1}}{\left(x^{1}+3\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{1}+3\right)\times 3x^{0}-\left(3x^{1}+14\right)x^{0}}{\left(x^{1}+3\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{1}\times 3x^{0}+3\times 3x^{0}-\left(3x^{1}x^{0}+14x^{0}\right)}{\left(x^{1}+3\right)^{2}}$$

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

$$\frac{3x^{1}+3\times 3x^{0}-\left(3x^{1}+14x^{0}\right)}{\left(x^{1}+3\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{3x^{1}+9x^{0}-\left(3x^{1}+14x^{0}\right)}{\left(x^{1}+3\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{3x^{1}+9x^{0}-3x^{1}-14x^{0}}{\left(x^{1}+3\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(3-3\right)x^{1}+\left(9-14\right)x^{0}}{\left(x^{1}+3\right)^{2}}$$

3 dan 3 ni va 9 dan 14 ni ayiring.

$$\frac{-5x^{0}}{\left(x^{1}+3\right)^{2}}$$

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

$$\frac{-5x^{0}}{\left(x+3\right)^{2}}$$

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

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