Whakaoti i te (frac{x^{-2}y^{3}}{x^{2}y})^-1/2(x^3y/y^1/2)^2

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

Aromātai

$$x^{8}$$

Ngā Upane Otinga

Me whakakore tahi te y i te taurunga me te tauraro.

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

Hei whakawehe i ngā pū o te pūtake kotahi, tangohia te taupū o te taurunga i te taupū o te tauraro.

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

Kia whakarewa i te \frac{y^{2}}{x^{4}} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

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

Me whakakore tahi te \sqrt{y} i te taurunga me te tauraro.

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

Whakarohaina te \left(\sqrt{y}x^{3}\right)^{2}.

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

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 3 me te 2 kia riro ai te 6.

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

Tātaihia te \sqrt{y} mā te pū o 2, kia riro ko y.

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

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 2 me te -\frac{1}{2} kia riro ai te -1.

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

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 4 me te -\frac{1}{2} kia riro ai te -2.

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

Tuhia te \frac{y^{-1}}{x^{-2}}y hei hautanga kotahi.

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

Tuhia te \frac{y^{-1}y}{x^{-2}}x^{6} hei hautanga kotahi.

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

Hei whakawehe i ngā pū o te pūtake kotahi, tangohia te taupū o te tauraro mai i te taupū o te taurunga.

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

Me whakakore te y me te y.

$$x^{8}$$

Kimi Pārōnaki e ai ki x

$$8x^{7}$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Pārōnaki

Me whakakore tahi te y i te taurunga me te tauraro.

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

Hei whakawehe i ngā pū o te pūtake kotahi, tangohia te taupū o te taurunga i te taupū o te tauraro.

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

Kia whakarewa i te \frac{y^{2}}{x^{4}} ki tētahi taupū, me whakarewa tahi te taurunga me te tauraro ki te taupū kātahi ka whakawehe.

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

Me whakakore tahi te \sqrt{y} i te taurunga me te tauraro.

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

Whakarohaina te \left(\sqrt{y}x^{3}\right)^{2}.

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

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 3 me te 2 kia riro ai te 6.

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

Tātaihia te \sqrt{y} mā te pū o 2, kia riro ko y.

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

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 2 me te -\frac{1}{2} kia riro ai te -1.

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

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 4 me te -\frac{1}{2} kia riro ai te -2.

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

Tuhia te \frac{y^{-1}}{x^{-2}}y hei hautanga kotahi.

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

Tuhia te \frac{y^{-1}y}{x^{-2}}x^{6} hei hautanga kotahi.

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

Hei whakawehe i ngā pū o te pūtake kotahi, tangohia te taupū o te tauraro mai i te taupū o te taurunga.

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

Me whakakore te y me te y.

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

Ko te pārōnaki o ax^{n} ko nax^{n-1}.

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

Tango 1 mai i 8.

$$8x^{7}$$