d/dxleft(x^2(1-2x)right) eching

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

Baholash

$$2x\left(1-3x\right)$$

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.

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

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

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

Qisqartirish.

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

-2x^{1}+1 ni 2x^{1} marotabaga ko'paytirish.

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

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

$$-2x^{2}-2\times 2x^{1+1}+2x^{1}$$

Qisqartirish.

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

O'xshash hadlarni birlashtirish.

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

-2 ni -4 ga qo'shish.

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

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

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

x ga nisbatan hosilani topish

$$2-12x$$