2x^2/x eching

$$\frac{ 2 { x }^{ 2 } }{ x }$$

x ga nisbatan hosilani topish

$$2$$

Koʻpaytma uchun derivativ qoidasidan foydalanish qadamlari

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

$$2x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x})+\frac{1}{x}\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2})$$

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

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

Qisqartirish.

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

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

$$-2x^{2-2}+4x^{-1+1}$$

Qisqartirish.

$$-2x^{0}+4x^{0}$$

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

$$-2+4\times 1$$

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

$$-2+4$$

Yechim qadamlari

Ayni asosning daraja ko'rsatkichi bo'lish uchun maxrajning darajasini surat darajasidan bo'ling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2}{1}x^{2-1})$$

Arifmetik hisobni amalga oshirish.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1})$$

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

$$2x^{1-1}$$

Arifmetik hisobni amalga oshirish.

$$2x^{0}$$

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

$$2\times 1$$

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

$$2$$

Baholash

$$2x$$

Yechim qadamlari

Surat va maxrajdagi ikkala x ni qisqartiring.

$$2x$$