d/dx(5x^3+3)/(2x+6) eching

$$\frac { d } { d x } \frac { ( 5 x ^ { 3 } + 3 ) } { ( 2 x + 6 ) }$$

Baholash

$$\frac{10x^{3}+45x^{2}-3}{2\left(x+3\right)^{2}}$$

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.

$$\frac{\left(2x^{1}+6\right)\frac{\mathrm{d}}{\mathrm{d}x}(5x^{3}+3)-\left(5x^{3}+3\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1}+6)}{\left(2x^{1}+6\right)^{2}}$$

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

$$\frac{\left(2x^{1}+6\right)\times 3\times 5x^{3-1}-\left(5x^{3}+3\right)\times 2x^{1-1}}{\left(2x^{1}+6\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(2x^{1}+6\right)\times 15x^{2}-\left(5x^{3}+3\right)\times 2x^{0}}{\left(2x^{1}+6\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{2x^{1}\times 15x^{2}+6\times 15x^{2}-\left(5x^{3}\times 2x^{0}+3\times 2x^{0}\right)}{\left(2x^{1}+6\right)^{2}}$$

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

$$\frac{2\times 15x^{1+2}+6\times 15x^{2}-\left(5\times 2x^{3}+3\times 2x^{0}\right)}{\left(2x^{1}+6\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{30x^{3}+90x^{2}-\left(10x^{3}+6x^{0}\right)}{\left(2x^{1}+6\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{30x^{3}+90x^{2}-10x^{3}-6x^{0}}{\left(2x^{1}+6\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(30-10\right)x^{3}+90x^{2}-6x^{0}}{\left(2x^{1}+6\right)^{2}}$$

30 dan 10 ni ayirish.

$$\frac{20x^{3}+90x^{2}-6x^{0}}{\left(2x^{1}+6\right)^{2}}$$

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

$$\frac{20x^{3}+90x^{2}-6x^{0}}{\left(2x+6\right)^{2}}$$

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

$$\frac{20x^{3}+90x^{2}-6\times 1}{\left(2x+6\right)^{2}}$$

Har qanday t sharti uchun t\times 1=t va 1t=t.

$$\frac{20x^{3}+90x^{2}-6}{\left(2x+6\right)^{2}}$$

x ga nisbatan hosilani topish

$$\frac{5x^{3}+45x^{2}+135x+3}{\left(x+3\right)^{3}}$$