x^3*{left(-1/xright)}^2 eching

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

Baholash

$$x$$

Ikki eksponentning koʻpaytmasi uchun qadamlar

Ifodani qisqartirish uchun eksponent qoidalaridan foydalanish.

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

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

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

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

$$1^{3}x^{3}x^{-2}$$

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

$$1^{3}x^{3-2}$$

3 va -2 belgilarini qo'shish.

$$1^{3}x^{1}$$

-1 ni 2 daraja ko'rsatgichiga oshirish.

$$x^{1}$$

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

$$x$$

x ga nisbatan hosilani topish

$$1$$

Derivativ ifodasidan foydalanish qadamlari

2 daraja ko‘rsatkichini -\frac{1}{x} ga hisoblang va \left(\frac{1}{x}\right)^{2} ni qiymatni oling.

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

\frac{1}{x}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\times \frac{1^{2}}{x^{2}})$$

x^{3}\times \frac{1^{2}}{x^{2}} ni yagona kasrga aylantiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{3}\times 1^{2}}{x^{2}})$$

Surat va maxrajdagi ikkala x^{2} ni qisqartiring.

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

2 daraja ko‘rsatkichini 1 ga hisoblang va 1 ni qiymatni oling.

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

ax^{n} hosilasi – nax^{n-1}.

$$x^{1-1}$$

1 dan 1 ni ayirish.

$$x^{0}$$

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

$$1$$