(3x^2y)^-1x^2z/3y^-1 eching

$$\frac { ( 3 x ^ { 2 } y ) ^ { - 1 } x ^ { 2 } z } { 3 y ^ { - 1 } }$$

Baholash

$$\frac{z}{9}$$

Yechim qadamlari

\left(3x^{2}y\right)^{-1} ni kengaytirish.

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

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va -1 ni ko‘paytirib, -2 ni oling.

$$\frac{3^{-1}x^{-2}y^{-1}x^{2}z}{3y^{-1}}$$

-1 daraja ko‘rsatkichini 3 ga hisoblang va \frac{1}{3} ni qiymatni oling.

$$\frac{\frac{1}{3}x^{-2}y^{-1}x^{2}z}{3y^{-1}}$$

1 hosil qilish uchun x^{-2} va x^{2} ni ko'paytirish.

$$\frac{\frac{1}{3}y^{-1}z}{3y^{-1}}$$

Surat va maxrajdagi ikkala \frac{1}{y} ni qisqartiring.

$$\frac{\frac{1}{3}z}{3}$$

\frac{1}{9}z ni olish uchun \frac{1}{3}z ni 3 ga bo‘ling.

$$\frac{1}{9}z$$

z ga nisbatan hosilani topish

$$\frac{1}{9} = 0,1111111111111111$$

Derivativ ifodasidan foydalanish qadamlari

\left(3x^{2}y\right)^{-1} ni kengaytirish.

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

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va -1 ni ko‘paytirib, -2 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{3^{-1}x^{-2}y^{-1}x^{2}z}{3y^{-1}})$$

-1 daraja ko‘rsatkichini 3 ga hisoblang va \frac{1}{3} ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{\frac{1}{3}x^{-2}y^{-1}x^{2}z}{3y^{-1}})$$

1 hosil qilish uchun x^{-2} va x^{2} ni ko'paytirish.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{\frac{1}{3}y^{-1}z}{3y^{-1}})$$

Surat va maxrajdagi ikkala \frac{1}{y} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{\frac{1}{3}z}{3})$$

\frac{1}{9}z ni olish uchun \frac{1}{3}z ni 3 ga bo‘ling.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{1}{9}z)$$

ax^{n} hosilasi – nax^{n-1}.

$$\frac{1}{9}z^{1-1}$$

1 dan 1 ni ayirish.

$$\frac{1}{9}z^{0}$$

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

$$\frac{1}{9}\times 1$$

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

$$\frac{1}{9}$$