(x^3+4/x^2)^prime eching

$$( \frac { x ^ { 3 } + 4 } { x ^ { 2 } } ) ^ { \prime }$$

Baholash

$$1-\frac{8}{x^{3}}$$

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.

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

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

$$\frac{x^{2}\times 3x^{3-1}-\left(x^{3}+4\right)\times 2x^{2-1}}{\left(x^{2}\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{x^{2}\times 3x^{2}-\left(x^{3}+4\right)\times 2x^{1}}{\left(x^{2}\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{2}\times 3x^{2}-\left(x^{3}\times 2x^{1}+4\times 2x^{1}\right)}{\left(x^{2}\right)^{2}}$$

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

$$\frac{3x^{2+2}-\left(2x^{3+1}+4\times 2x^{1}\right)}{\left(x^{2}\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{3x^{4}-\left(2x^{4}+8x^{1}\right)}{\left(x^{2}\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{3x^{4}-2x^{4}-8x^{1}}{\left(x^{2}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(3-2\right)x^{4}-8x^{1}}{\left(x^{2}\right)^{2}}$$

3 dan 2 ni ayirish.

$$\frac{x^{4}-8x^{1}}{\left(x^{2}\right)^{2}}$$

x omili.

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

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

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

2 ni 2 marotabaga ko'paytirish.

$$\frac{x\left(x^{3}-8x^{0}\right)}{x^{4}}$$

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

$$\frac{x^{3}-8x^{0}}{x^{4-1}}$$

4 dan 1 ni ayirish.

$$\frac{x^{3}-8x^{0}}{x^{3}}$$

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

$$\frac{x^{3}-8\times 1}{x^{3}}$$

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

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

x ga nisbatan hosilani topish

$$\frac{24}{x^{4}}$$