Whakaoti i te 3x^0/y+2y^-1-y^-3/y^-2

$$\frac { 3 x ^ { 0 } } { y } + 2 y ^ { - 1 } - \frac { y ^ { - 3 } } { y ^ { - 2 } }$$

Aromātai

$$\frac{4}{y}$$

Ngā Hipanga Rongoā Poto

Tuhia anō te y^{-2} hei y^{-3}y. Me whakakore tahi te y^{-3} i te taurunga me te tauraro.

$$\frac{3x^{0}}{y}+2y^{-1}-\frac{1}{y}$$

Tātaihia te x mā te pū o 0, kia riro ko 1.

$$\frac{3\times 1}{y}+2y^{-1}-\frac{1}{y}$$

Whakareatia te 3 ki te 1, ka 3.

$$\frac{3}{y}+2y^{-1}-\frac{1}{y}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 2y^{-1} ki te \frac{y}{y}.

$$\frac{3}{y}+\frac{2y^{-1}y}{y}-\frac{1}{y}$$

Tā te mea he rite te tauraro o \frac{3}{y} me \frac{2y^{-1}y}{y}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{3+2y^{-1}y}{y}-\frac{1}{y}$$

Mahia ngā whakarea i roto o 3+2y^{-1}y.

$$\frac{3+2}{y}-\frac{1}{y}$$

Mahia ngā tātaitai i roto o 3+2.

$$\frac{5}{y}-\frac{1}{y}$$

Tā te mea he rite te tauraro o \frac{5}{y} me \frac{1}{y}, me tango rāua mā te tango i ō raua taurunga. Tangohia te 1 i te 5, ka 4.

$$\frac{4}{y}$$

Kimi Pārōnaki e ai ki y

$$-\frac{4}{y^{2}}$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Pārōnaki

Tuhia anō te y^{-2} hei y^{-3}y. Me whakakore tahi te y^{-3} i te taurunga me te tauraro.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3x^{0}}{y}+2y^{-1}-\frac{1}{y})$$

Tātaihia te x mā te pū o 0, kia riro ko 1.

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

Whakareatia te 3 ki te 1, ka 3.

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 2y^{-1} ki te \frac{y}{y}.

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

Tā te mea he rite te tauraro o \frac{3}{y} me \frac{2y^{-1}y}{y}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Mahia ngā whakarea i roto o 3+2y^{-1}y.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{3+2}{y}-\frac{1}{y})$$

Mahia ngā tātaitai i roto o 3+2.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{5}{y}-\frac{1}{y})$$

Tā te mea he rite te tauraro o \frac{5}{y} me \frac{1}{y}, me tango rāua mā te tango i ō raua taurunga. Tangohia te 1 i te 5, ka 4.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{4}{y})$$

Ko te pārōnaki o ax^{n} ko nax^{n-1}.

$$-4y^{-1-1}$$

Tango 1 mai i -1.

$$-4y^{-2}$$