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

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

Baholash

$$\frac{1}{2}-\frac{4}{x^{3}}$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Ifodalarni qo‘shish yoki ayirish uchun ularni yoyib, maxrajlarini bir xil qiling. 2 va x^{2} ning eng kichik umumiy karralisi 2x^{2}. \frac{x}{2} ni \frac{x^{2}}{x^{2}} marotabaga ko'paytirish. \frac{2}{x^{2}} ni \frac{2}{2} marotabaga ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{xx^{2}}{2x^{2}}+\frac{2\times 2}{2x^{2}})$$

\frac{xx^{2}}{2x^{2}} va \frac{2\times 2}{2x^{2}} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{xx^{2}+2\times 2}{2x^{2}})$$

xx^{2}+2\times 2 ichidagi ko‘paytirishlarni bajaring.

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

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

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

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

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

Arifmetik hisobni amalga oshirish.

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

Distributiv xususiyatdan foydalanib kengaytirish.

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

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

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

Arifmetik hisobni amalga oshirish.

$$\frac{6x^{4}-\left(4x^{4}+16x^{1}\right)}{\left(2x^{2}\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{6x^{4}-4x^{4}-16x^{1}}{\left(2x^{2}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(6-4\right)x^{4}-16x^{1}}{\left(2x^{2}\right)^{2}}$$

6 dan 4 ni ayirish.

$$\frac{2x^{4}-16x^{1}}{\left(2x^{2}\right)^{2}}$$

2x omili.

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

Ikki yoki undan ko'p raqam koʻpaytmasini daraja ko'rsatkichiga oshirish uchun har bir raqamni daraja ko'rsatkichiga oshiring va ularning koʻpaytmasini chiqaring.

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

2 ni 2 daraja ko'rsatgichiga oshirish.

$$\frac{2x\left(x^{3}-8x^{0}\right)}{4\left(x^{2}\right)^{2}}$$

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

$$\frac{2x\left(x^{3}-8x^{0}\right)}{4x^{2\times 2}}$$

2 ni 2 marotabaga ko'paytirish.

$$\frac{2x\left(x^{3}-8x^{0}\right)}{4x^{4}}$$

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

$$\frac{2\left(x^{3}-8x^{0}\right)}{4x^{4-1}}$$

4 dan 1 ni ayirish.

$$\frac{2\left(x^{3}-8x^{0}\right)}{4x^{3}}$$

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

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

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

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

x ga nisbatan hosilani topish

$$\frac{12}{x^{4}}$$