Whakaoti i te 3z/12z^2

$$\frac { 3 z } { 12 z ^ { 2 } }$$

Aromātai

$$\frac{1}{4z}$$

Ngā Upane mō te Hua o ngā Pānga Taupū e Rua

Whakamahia ngā ture taupū hei whakarūnā i te kīanga.

$$\left(3z^{1}\right)^{1}\times \frac{1}{12z^{2}}$$

Hei hiki i te hua o ngā tau e rua, neke atu rānei ki tētahi pū, hīkina ia tau ki te pū ka tuhi ko tāna hua.

$$3^{1}\left(z^{1}\right)^{1}\times \frac{1}{12}\times \frac{1}{z^{2}}$$

Whakamahia te Āhuatanga Kōaro o te Whakareanga.

$$3^{1}\times \frac{1}{12}\left(z^{1}\right)^{1}\times \frac{1}{z^{2}}$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū.

$$3^{1}\times \frac{1}{12}z^{1}z^{2\left(-1\right)}$$

Whakareatia 2 ki te -1.

$$3^{1}\times \frac{1}{12}z^{1}z^{-2}$$

Hei whakarea pū o te pūtake ōrite, tāpiri ana taupū.

$$3^{1}\times \frac{1}{12}z^{1-2}$$

Tāpirihia ngā taupū 1 me -2.

$$3^{1}\times \frac{1}{12}\times \frac{1}{z}$$

Hīkina te 3 ki te pū 1.

$$3\times \frac{1}{12}\times \frac{1}{z}$$

Whakareatia 3 ki te \frac{1}{12}.

$$\frac{1}{4}\times \frac{1}{z}$$

Ngā Upane mō te Otinga o ngā Pānga Taupū

Whakamahia ngā ture taupū hei whakarūnā i te kīanga.

$$\frac{3^{1}z^{1}}{12^{1}z^{2}}$$

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

$$\frac{3^{1}z^{1-2}}{12^{1}}$$

Tango 2 mai i 1.

$$\frac{3^{1}\times \frac{1}{z}}{12^{1}}$$

Whakahekea te hautanga \frac{3}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{1}{4}\times \frac{1}{z}$$

Kimi Pārōnaki e ai ki z

$$-\frac{1}{4z^{2}}$$

Ngā Upane Otinga

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

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{3}{12}z^{1-2})$$

Mahia ngā tātaitanga.

$$\frac{\mathrm{d}}{\mathrm{d}z}(\frac{1}{4}\times \frac{1}{z})$$

Ko te pārōnaki o tētahi pūrau ko te tapeke o ngā pārōnaki o ōna kīanga tau. Ko te pārōnaki o tētahi kīanga tau pūmau ko 0. Ko te pārōnaki o te ax^{n} ko te nax^{n-1}.

$$-\frac{1}{4}z^{-1-1}$$

Mahia ngā tātaitanga.

$$-\frac{1}{4}z^{-2}$$