(frac{x^{-2}y^{3}}{x^{2}y})^-1/2(x^3y/y^1/2)^2 eching

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

Baholash

$$x^{8}$$

Yechim qadamlari

Surat va maxrajdagi ikkala y ni qisqartiring.

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

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun suratning darajasini maxraj darajasiga bo‘ling.

$$\left(\frac{y^{2}}{x^{4}}\right)^{-\frac{1}{2}}\times \left(\frac{x^{3}y}{y^{\frac{1}{2}}}\right)^{2}$$

\frac{y^{2}}{x^{4}}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\left(y^{2}\right)^{-\frac{1}{2}}}{\left(x^{4}\right)^{-\frac{1}{2}}}\times \left(\frac{x^{3}y}{y^{\frac{1}{2}}}\right)^{2}$$

Surat va maxrajdagi ikkala \sqrt{y} ni qisqartiring.

$$\frac{\left(y^{2}\right)^{-\frac{1}{2}}}{\left(x^{4}\right)^{-\frac{1}{2}}}\left(\sqrt{y}x^{3}\right)^{2}$$

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

$$\frac{\left(y^{2}\right)^{-\frac{1}{2}}}{\left(x^{4}\right)^{-\frac{1}{2}}}\left(\sqrt{y}\right)^{2}\left(x^{3}\right)^{2}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 2 ni ko‘paytirib, 6 ni oling.

$$\frac{\left(y^{2}\right)^{-\frac{1}{2}}}{\left(x^{4}\right)^{-\frac{1}{2}}}\left(\sqrt{y}\right)^{2}x^{6}$$

2 daraja ko‘rsatkichini \sqrt{y} ga hisoblang va y ni qiymatni oling.

$$\frac{\left(y^{2}\right)^{-\frac{1}{2}}}{\left(x^{4}\right)^{-\frac{1}{2}}}yx^{6}$$

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

$$\frac{y^{-1}}{\left(x^{4}\right)^{-\frac{1}{2}}}yx^{6}$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 4 va -\frac{1}{2} ni ko‘paytirib, -2 ni oling.

$$\frac{y^{-1}}{x^{-2}}yx^{6}$$

\frac{y^{-1}}{x^{-2}}y ni yagona kasrga aylantiring.

$$\frac{y^{-1}y}{x^{-2}}x^{6}$$

\frac{y^{-1}y}{x^{-2}}x^{6} ni yagona kasrga aylantiring.

$$\frac{y^{-1}yx^{6}}{x^{-2}}$$

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

$$\frac{1}{y}yx^{8}$$

y va y ni qisqartiring.

$$x^{8}$$

x ga nisbatan hosilani topish

$$8x^{7}$$

Derivativ ifodasidan foydalanish qadamlari

Surat va maxrajdagi ikkala y ni qisqartiring.

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

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun suratning darajasini maxraj darajasiga bo‘ling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(\frac{y^{2}}{x^{4}}\right)^{-\frac{1}{2}}\times \left(\frac{x^{3}y}{y^{\frac{1}{2}}}\right)^{2})$$

\frac{y^{2}}{x^{4}}ni darajaga oshirish uchun, surat va maxrajni darajaga oshirib, keyin bo‘ling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(y^{2}\right)^{-\frac{1}{2}}}{\left(x^{4}\right)^{-\frac{1}{2}}}\times \left(\frac{x^{3}y}{y^{\frac{1}{2}}}\right)^{2})$$

Surat va maxrajdagi ikkala \sqrt{y} ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(y^{2}\right)^{-\frac{1}{2}}}{\left(x^{4}\right)^{-\frac{1}{2}}}\left(\sqrt{y}x^{3}\right)^{2})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(y^{2}\right)^{-\frac{1}{2}}}{\left(x^{4}\right)^{-\frac{1}{2}}}\left(\sqrt{y}\right)^{2}\left(x^{3}\right)^{2})$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 2 ni ko‘paytirib, 6 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(y^{2}\right)^{-\frac{1}{2}}}{\left(x^{4}\right)^{-\frac{1}{2}}}\left(\sqrt{y}\right)^{2}x^{6})$$

2 daraja ko‘rsatkichini \sqrt{y} ga hisoblang va y ni qiymatni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(y^{2}\right)^{-\frac{1}{2}}}{\left(x^{4}\right)^{-\frac{1}{2}}}yx^{6})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{y^{-1}}{\left(x^{4}\right)^{-\frac{1}{2}}}yx^{6})$$

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 4 va -\frac{1}{2} ni ko‘paytirib, -2 ni oling.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{y^{-1}}{x^{-2}}yx^{6})$$

\frac{y^{-1}}{x^{-2}}y ni yagona kasrga aylantiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{y^{-1}y}{x^{-2}}x^{6})$$

\frac{y^{-1}y}{x^{-2}}x^{6} ni yagona kasrga aylantiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{y^{-1}yx^{6}}{x^{-2}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{y}yx^{8})$$

y va y ni qisqartiring.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{8})$$

ax^{n} hosilasi – nax^{n-1}.

$$8x^{8-1}$$

8 dan 1 ni ayirish.

$$8x^{7}$$