f(x)=2/x+3-5 eching

$$f ( x ) = \frac { 2 } { x + 3 } - 5$$

Baholash

$$-\frac{5x+13}{x+3}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 5 ni \frac{x+3}{x+3} marotabaga ko'paytirish.

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

\frac{2}{x+3} va \frac{5\left(x+3\right)}{x+3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

2-5\left(x+3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{2-5x-15}{x+3}$$

2-5x-15 kabi iboralarga o‘xshab birlashtiring.

$$\frac{-13-5x}{x+3}$$

x ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 5 ni \frac{x+3}{x+3} marotabaga ko'paytirish.

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

\frac{2}{x+3} va \frac{5\left(x+3\right)}{x+3} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

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

2-5\left(x+3\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2-5x-15}{x+3})$$

2-5x-15 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{-13-5x}{x+3})$$

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

$$\frac{\left(x^{1}+3\right)\frac{\mathrm{d}}{\mathrm{d}x}(-5x^{1}-13)-\left(-5x^{1}-13\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}+3)}{\left(x^{1}+3\right)^{2}}$$

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

$$\frac{\left(x^{1}+3\right)\left(-5\right)x^{1-1}-\left(-5x^{1}-13\right)x^{1-1}}{\left(x^{1}+3\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{1}+3\right)\left(-5\right)x^{0}-\left(-5x^{1}-13\right)x^{0}}{\left(x^{1}+3\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{1}\left(-5\right)x^{0}+3\left(-5\right)x^{0}-\left(-5x^{1}x^{0}-13x^{0}\right)}{\left(x^{1}+3\right)^{2}}$$

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

$$\frac{-5x^{1}+3\left(-5\right)x^{0}-\left(-5x^{1}-13x^{0}\right)}{\left(x^{1}+3\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{-5x^{1}-15x^{0}-\left(-5x^{1}-13x^{0}\right)}{\left(x^{1}+3\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{-5x^{1}-15x^{0}-\left(-5x^{1}\right)-\left(-13x^{0}\right)}{\left(x^{1}+3\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(-5-\left(-5\right)\right)x^{1}+\left(-15-\left(-13\right)\right)x^{0}}{\left(x^{1}+3\right)^{2}}$$

-5 dan -5 ni va -15 dan -13 ni ayiring.

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

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

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

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

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