5/(x+1)-2/17-3 eching

$$\frac { 5 } { ( x + 1 ) } - \frac { 2 } { 17 - 3 }$$

Baholash

$$\frac{34-x}{7\left(x+1\right)}$$

Qisqa yechim qadamlari

14 olish uchun 17 dan 3 ni ayirish.

$$\frac{5}{x+1}-\frac{2}{14}$$

\frac{2}{14} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{5}{x+1}-\frac{1}{7}$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x+1 va 7 ning eng kichik umumiy karralisi 7\left(x+1\right). \frac{5}{x+1} ni \frac{7}{7} marotabaga ko'paytirish. \frac{1}{7} ni \frac{x+1}{x+1} marotabaga ko'paytirish.

$$\frac{5\times 7}{7\left(x+1\right)}-\frac{x+1}{7\left(x+1\right)}$$

\frac{5\times 7}{7\left(x+1\right)} va \frac{x+1}{7\left(x+1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{5\times 7-\left(x+1\right)}{7\left(x+1\right)}$$

5\times 7-\left(x+1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{35-x-1}{7\left(x+1\right)}$$

35-x-1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{34-x}{7\left(x+1\right)}$$

7\left(x+1\right) ni kengaytirish.

$$\frac{34-x}{7x+7}$$

x ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

14 olish uchun 17 dan 3 ni ayirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{x+1}-\frac{2}{14})$$

\frac{2}{14} ulushini 2 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{x+1}-\frac{1}{7})$$

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. x+1 va 7 ning eng kichik umumiy karralisi 7\left(x+1\right). \frac{5}{x+1} ni \frac{7}{7} marotabaga ko'paytirish. \frac{1}{7} ni \frac{x+1}{x+1} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\times 7}{7\left(x+1\right)}-\frac{x+1}{7\left(x+1\right)})$$

\frac{5\times 7}{7\left(x+1\right)} va \frac{x+1}{7\left(x+1\right)} da bir xil maxraji bor, ularning suratini ayirish orqali ayiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5\times 7-\left(x+1\right)}{7\left(x+1\right)})$$

5\times 7-\left(x+1\right) ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{35-x-1}{7\left(x+1\right)})$$

35-x-1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{34-x}{7\left(x+1\right)})$$

7 ga x+1 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{34-x}{7x+7})$$

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

$$\frac{\left(7x^{1}+7\right)\frac{\mathrm{d}}{\mathrm{d}x}(-x^{1}+34)-\left(-x^{1}+34\right)\frac{\mathrm{d}}{\mathrm{d}x}(7x^{1}+7)}{\left(7x^{1}+7\right)^{2}}$$

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

$$\frac{\left(7x^{1}+7\right)\left(-1\right)x^{1-1}-\left(-x^{1}+34\right)\times 7x^{1-1}}{\left(7x^{1}+7\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(7x^{1}+7\right)\left(-1\right)x^{0}-\left(-x^{1}+34\right)\times 7x^{0}}{\left(7x^{1}+7\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{7x^{1}\left(-1\right)x^{0}+7\left(-1\right)x^{0}-\left(-x^{1}\times 7x^{0}+34\times 7x^{0}\right)}{\left(7x^{1}+7\right)^{2}}$$

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

$$\frac{7\left(-1\right)x^{1}+7\left(-1\right)x^{0}-\left(-7x^{1}+34\times 7x^{0}\right)}{\left(7x^{1}+7\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{-7x^{1}-7x^{0}-\left(-7x^{1}+238x^{0}\right)}{\left(7x^{1}+7\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{-7x^{1}-7x^{0}-\left(-7x^{1}\right)-238x^{0}}{\left(7x^{1}+7\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(-7-\left(-7\right)\right)x^{1}+\left(-7-238\right)x^{0}}{\left(7x^{1}+7\right)^{2}}$$

-7 dan -7 ni va -7 dan 238 ni ayiring.

$$\frac{-245x^{0}}{\left(7x^{1}+7\right)^{2}}$$

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

$$\frac{-245x^{0}}{\left(7x+7\right)^{2}}$$

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

$$\frac{-245}{\left(7x+7\right)^{2}}$$