x^3/x^3+16 eching

$$\frac{ { x }^{ 3 } }{ { x }^{ 3 } +16 }$$

x ga nisbatan hosilani topish

$$48\times \left(\frac{x}{x^{3}+16}\right)^{2}$$

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.

$$\frac{\left(x^{3}+16\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{3})-x^{3}\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}+16)}{\left(x^{3}+16\right)^{2}}$$

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

$$\frac{\left(x^{3}+16\right)\times 3x^{3-1}-x^{3}\times 3x^{3-1}}{\left(x^{3}+16\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{\left(x^{3}+16\right)\times 3x^{2}-x^{3}\times 3x^{2}}{\left(x^{3}+16\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{3}\times 3x^{2}+16\times 3x^{2}-x^{3}\times 3x^{2}}{\left(x^{3}+16\right)^{2}}$$

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

$$\frac{3x^{3+2}+16\times 3x^{2}-3x^{3+2}}{\left(x^{3}+16\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{3x^{5}+48x^{2}-3x^{5}}{\left(x^{3}+16\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(3-3\right)x^{5}+48x^{2}}{\left(x^{3}+16\right)^{2}}$$

3 dan 3 ni ayirish.

$$\frac{48x^{2}}{\left(x^{3}+16\right)^{2}}$$

Baholash

$$\frac{x^{3}}{x^{3}+16}$$