4+1/x-3 eching

$$4+ \frac{ 1 }{ x-3 }$$

Baholash

$$\frac{4x-11}{x-3}$$

Qisqa yechim qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 4 ni \frac{x-3}{x-3} marotabaga ko'paytirish.

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

\frac{4\left(x-3\right)}{x-3} va \frac{1}{x-3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

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

$$\frac{4x-12+1}{x-3}$$

4x-12+1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{4x-11}{x-3}$$

x ga nisbatan hosilani topish

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

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 4 ni \frac{x-3}{x-3} marotabaga ko'paytirish.

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

\frac{4\left(x-3\right)}{x-3} va \frac{1}{x-3} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x-12+1}{x-3})$$

4x-12+1 kabi iboralarga o‘xshab birlashtiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4x-11}{x-3})$$

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

$$\frac{\left(x^{1}-3\right)\frac{\mathrm{d}}{\mathrm{d}x}(4x^{1}-11)-\left(4x^{1}-11\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-3)}{\left(x^{1}-3\right)^{2}}$$

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

$$\frac{\left(x^{1}-3\right)\times 4x^{1-1}-\left(4x^{1}-11\right)x^{1-1}}{\left(x^{1}-3\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{1}-3\right)\times 4x^{0}-\left(4x^{1}-11\right)x^{0}}{\left(x^{1}-3\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{1}\times 4x^{0}-3\times 4x^{0}-\left(4x^{1}x^{0}-11x^{0}\right)}{\left(x^{1}-3\right)^{2}}$$

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

$$\frac{4x^{1}-3\times 4x^{0}-\left(4x^{1}-11x^{0}\right)}{\left(x^{1}-3\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{4x^{1}-12x^{0}-\left(4x^{1}-11x^{0}\right)}{\left(x^{1}-3\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{4x^{1}-12x^{0}-4x^{1}-\left(-11x^{0}\right)}{\left(x^{1}-3\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(4-4\right)x^{1}+\left(-12-\left(-11\right)\right)x^{0}}{\left(x^{1}-3\right)^{2}}$$

4 dan 4 ni va -12 dan -11 ni ayiring.

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

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

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

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

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