Whakaoti i te 54v^4/9v^5

$$\frac { 54 v ^ { 4 } } { 9 v ^ { 5 } }$$

Aromātai

$$\frac{6}{v}$$

Ngā Upane mō te Hua o ngā Pānga Taupū e Rua

Whakamahia ngā ture taupū hei whakarūnā i te kīanga.

$$\left(54v^{4}\right)^{1}\times \frac{1}{9v^{5}}$$

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.

$$54^{1}\left(v^{4}\right)^{1}\times \frac{1}{9}\times \frac{1}{v^{5}}$$

Whakamahia te Āhuatanga Kōaro o te Whakareanga.

$$54^{1}\times \frac{1}{9}\left(v^{4}\right)^{1}\times \frac{1}{v^{5}}$$

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

$$54^{1}\times \frac{1}{9}v^{4}v^{5\left(-1\right)}$$

Whakareatia 5 ki te -1.

$$54^{1}\times \frac{1}{9}v^{4}v^{-5}$$

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

$$54^{1}\times \frac{1}{9}v^{4-5}$$

Tāpirihia ngā taupū 4 me -5.

$$54^{1}\times \frac{1}{9}\times \frac{1}{v}$$

Hīkina te 54 ki te pū 1.

$$54\times \frac{1}{9}\times \frac{1}{v}$$

Whakareatia 54 ki te \frac{1}{9}.

$$6\times \frac{1}{v}$$

Ngā Upane mō te Otinga o ngā Pānga Taupū

Whakamahia ngā ture taupū hei whakarūnā i te kīanga.

$$\frac{54^{1}v^{4}}{9^{1}v^{5}}$$

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

$$\frac{54^{1}v^{4-5}}{9^{1}}$$

Tango 5 mai i 4.

$$\frac{54^{1}\times \frac{1}{v}}{9^{1}}$$

Whakawehe 54 ki te 9.

$$6\times \frac{1}{v}$$

Kimi Pārōnaki e ai ki v

$$-\frac{6}{v^{2}}$$

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.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{54}{9}v^{4-5})$$

Mahia ngā tātaitanga.

$$\frac{\mathrm{d}}{\mathrm{d}v}(6\times \frac{1}{v})$$

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}.

$$-6v^{-1-1}$$

Mahia ngā tātaitanga.

$$-6v^{-2}$$