2x^3/9+x^3 eching

$$\frac { 2 x ^ { 3 } } { 9 + x ^ { 3 } }$$

x ga nisbatan hosilani topish

$$54\times \left(\frac{x}{x^{3}+9}\right)^{2}$$

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.

$$\frac{\left(x^{3}+9\right)\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3})-2x^{3}\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}+9)}{\left(x^{3}+9\right)^{2}}$$

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

$$\frac{\left(x^{3}+9\right)\times 3\times 2x^{3-1}-2x^{3}\times 3x^{3-1}}{\left(x^{3}+9\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{3}+9\right)\times 6x^{2}-2x^{3}\times 3x^{2}}{\left(x^{3}+9\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{3}\times 6x^{2}+9\times 6x^{2}-2x^{3}\times 3x^{2}}{\left(x^{3}+9\right)^{2}}$$

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

$$\frac{6x^{3+2}+9\times 6x^{2}-2\times 3x^{3+2}}{\left(x^{3}+9\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{6x^{5}+54x^{2}-6x^{5}}{\left(x^{3}+9\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(6-6\right)x^{5}+54x^{2}}{\left(x^{3}+9\right)^{2}}$$

6 dan 6 ni ayirish.

$$\frac{54x^{2}}{\left(x^{3}+9\right)^{2}}$$

Baholash

$$\frac{2x^{3}}{x^{3}+9}$$