d/dxleft(3x^2-1/x-3right) eching

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

Baholash

$$\frac{3x^{2}-18x+1}{\left(x-3\right)^{2}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

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

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Arifmetik hisobni amalga oshirish.

$$\frac{6x^{2}-18x^{1}-\left(3x^{2}-x^{0}\right)}{\left(x^{1}-3\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{6x^{2}-18x^{1}-3x^{2}-\left(-x^{0}\right)}{\left(x^{1}-3\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(6-3\right)x^{2}-18x^{1}-\left(-x^{0}\right)}{\left(x^{1}-3\right)^{2}}$$

6 dan 3 ni ayirish.

$$\frac{3x^{2}-18x^{1}-\left(-x^{0}\right)}{\left(x^{1}-3\right)^{2}}$$

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

$$\frac{3x^{2}-18x-\left(-x^{0}\right)}{\left(x-3\right)^{2}}$$

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

$$\frac{3x^{2}-18x-\left(-1\right)}{\left(x-3\right)^{2}}$$

x ga nisbatan hosilani topish

$$\frac{52}{\left(x-3\right)^{3}}$$