(x^2/x)^prime eching

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

Baholash

$$1$$

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.

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

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

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

Qisqartirish.

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

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

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

Qisqartirish.

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

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

$$-1+2\times 1$$

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

$$-1+2$$

Yechim qadamlari

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

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

Arifmetik hisobni amalga oshirish.

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

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

$$x^{1-1}$$

Arifmetik hisobni amalga oshirish.

$$x^{0}$$

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

$$1$$

x ga nisbatan hosilani topish

$$0$$