d/dxleft(2x^2+10000x/x^2right) eching

$$\frac{d}{d x } \left(2 { x }^{ 2 } + \frac{ 10000x }{ { x }^{ 2 } } \right)$$

Baholash

$$4x-\frac{10000}{x^{2}}$$

Koʻpaytma uchun derivativ qoidasidan foydalanish qadamlari

Surat va maxrajdagi ikkala x ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}+\frac{10000}{x})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{2}x}{x}+\frac{10000}{x})$$

\frac{2x^{2}x}{x} va \frac{10000}{x} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{2}x+10000}{x})$$

2x^{2}x+10000 ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{3}+10000}{x})$$

Har qanday ikki differensial funksiya uchun, ikki funksiya koʻpaytmasining hosilasi birinchi funksiya marotabasi, ikkinchi plyus hosilasi ikkinchi funksiya marotabasi birinchining hosilasidir.

$$\left(2x^{3}+10000\right)\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x})+\frac{1}{x}\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+10000)$$

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

$$\left(2x^{3}+10000\right)\left(-1\right)x^{-1-1}+\frac{1}{x}\times 3\times 2x^{3-1}$$

Qisqartirish.

$$\left(2x^{3}+10000\right)\left(-1\right)x^{-2}+\frac{1}{x}\times 6x^{2}$$

2x^{3}+10000 ni -x^{-2} marotabaga ko'paytirish.

$$2x^{3}\left(-1\right)x^{-2}+10000\left(-1\right)x^{-2}+\frac{1}{x}\times 6x^{2}$$

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

$$-2x^{3-2}-10000x^{-2}+6x^{-1+2}$$

Qisqartirish.

$$-2x^{1}-10000x^{-2}+6x^{1}$$

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

$$-2x-10000x^{-2}+6x$$

Koeffitsient uchun derivativ qoidasidan foydalanish qadamlari

Surat va maxrajdagi ikkala x ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}+\frac{10000}{x})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{2}x}{x}+\frac{10000}{x})$$

\frac{2x^{2}x}{x} va \frac{10000}{x} da bir xil maxraji bor, ularning suratini qo‘shish orqali qo‘shing.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{2}x+10000}{x})$$

2x^{2}x+10000 ichidagi ko‘paytirishlarni bajaring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{3}+10000}{x})$$

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

$$\frac{x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+10000)-\left(2x^{3}+10000\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1})}{\left(x^{1}\right)^{2}}$$

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

$$\frac{x^{1}\times 3\times 2x^{3-1}-\left(2x^{3}+10000\right)x^{1-1}}{\left(x^{1}\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{x^{1}\times 6x^{2}-\left(2x^{3}+10000\right)x^{0}}{\left(x^{1}\right)^{2}}$$

Distributiv xususiyatdan foydalanib kengaytirish.

$$\frac{x^{1}\times 6x^{2}-\left(2x^{3}x^{0}+10000x^{0}\right)}{\left(x^{1}\right)^{2}}$$

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

$$\frac{6x^{1+2}-\left(2x^{3}+10000x^{0}\right)}{\left(x^{1}\right)^{2}}$$

Arifmetik hisobni amalga oshirish.

$$\frac{6x^{3}-\left(2x^{3}+10000x^{0}\right)}{\left(x^{1}\right)^{2}}$$

Keraksiz qavslarni olib tashlash.

$$\frac{6x^{3}-2x^{3}-10000x^{0}}{\left(x^{1}\right)^{2}}$$

O'xshash hadlarni birlashtirish.

$$\frac{\left(6-2\right)x^{3}-10000x^{0}}{\left(x^{1}\right)^{2}}$$

6 dan 2 ni ayirish.

$$\frac{4x^{3}-10000x^{0}}{\left(x^{1}\right)^{2}}$$

4 omili.

$$\frac{4\left(x^{3}-2500x^{0}\right)}{\left(x^{1}\right)^{2}}$$

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

$$\frac{4\left(x^{3}-2500x^{0}\right)}{1^{2}x^{2}}$$

1 ni 2 daraja ko'rsatgichiga oshirish.

$$\frac{4\left(x^{3}-2500x^{0}\right)}{x^{2}}$$

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

$$\frac{4\left(x^{3}-2500\times 1\right)}{x^{2}}$$

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

$$\frac{4\left(x^{3}-2500\right)}{x^{2}}$$

x ga nisbatan hosilani topish

$$4+\frac{20000}{x^{3}}$$