2xdiv3x^3/x-4 eching

$$2 x \div \frac { 3 x ^ { 3 } } { x - 4 }$$

Baholash

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

Qisqa yechim qadamlari

2x ni \frac{3x^{3}}{x-4} ga bo'lish 2x ga k'paytirish \frac{3x^{3}}{x-4} ga qaytarish.

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

Surat va maxrajdagi ikkala x ni qisqartiring.

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

2 ga x-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{2x-8}{3x^{2}}$$

x ga nisbatan hosilani topish

$$\frac{2\left(8-x\right)}{3x^{3}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

2x ni \frac{3x^{3}}{x-4} ga bo'lish 2x ga k'paytirish \frac{3x^{3}}{x-4} ga qaytarish.

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

Surat va maxrajdagi ikkala x ni qisqartiring.

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

2 ga x-4 ni ko'paytirish orqali distributiv xususiyatdan foydalanish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x-8}{3x^{2}})$$

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

$$\frac{3x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1}-8)-\left(2x^{1}-8\right)\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2})}{\left(3x^{2}\right)^{2}}$$

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

$$\frac{3x^{2}\times 2x^{1-1}-\left(2x^{1}-8\right)\times 2\times 3x^{2-1}}{\left(3x^{2}\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{3x^{2}\times 2x^{0}-\left(2x^{1}-8\right)\times 6x^{1}}{\left(3x^{2}\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{3x^{2}\times 2x^{0}-\left(2x^{1}\times 6x^{1}-8\times 6x^{1}\right)}{\left(3x^{2}\right)^{2}}$$

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

$$\frac{3\times 2x^{2}-\left(2\times 6x^{1+1}-8\times 6x^{1}\right)}{\left(3x^{2}\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{6x^{2}-\left(12x^{2}-48x^{1}\right)}{\left(3x^{2}\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{6x^{2}-12x^{2}-\left(-48x^{1}\right)}{\left(3x^{2}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(6-12\right)x^{2}-\left(-48x^{1}\right)}{\left(3x^{2}\right)^{2}}$$

6 dan 12 ni ayirish.

$$\frac{-6x^{2}-\left(-48x^{1}\right)}{\left(3x^{2}\right)^{2}}$$

6x omili.

$$\frac{6x\left(-x^{1}-\left(-8x^{0}\right)\right)}{\left(3x^{2}\right)^{2}}$$

Ikki yoki undan ko'p raqam koʻpaytmasini daraja ko'rsatkichiga oshirish uchun har bir raqamni daraja ko'rsatkichiga oshiring va ularning koʻpaytmasini chiqaring.

$$\frac{6x\left(-x^{1}-\left(-8x^{0}\right)\right)}{3^{2}\left(x^{2}\right)^{2}}$$

3 ni 2 daraja ko'rsatgichiga oshirish.

$$\frac{6x\left(-x^{1}-\left(-8x^{0}\right)\right)}{9\left(x^{2}\right)^{2}}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring.

$$\frac{6x\left(-x^{1}-\left(-8x^{0}\right)\right)}{9x^{2\times 2}}$$

2 ni 2 marotabaga ko'paytirish.

$$\frac{6x\left(-x^{1}-\left(-8x^{0}\right)\right)}{9x^{4}}$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun suratning darajasini maxraj darajasiga bo‘ling.

$$\frac{6\left(-x^{1}-\left(-8x^{0}\right)\right)}{9x^{4-1}}$$

4 dan 1 ni ayirish.

$$\frac{6\left(-x^{1}-\left(-8x^{0}\right)\right)}{9x^{3}}$$

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

$$\frac{6\left(-x-\left(-8x^{0}\right)\right)}{9x^{3}}$$

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

$$\frac{6\left(-x-\left(-8\right)\right)}{9x^{3}}$$