Whakaoti i te frac{(9)^{3}*27*t^4}{(3)^2*(3)^4*t^2}

$$\frac { ( 9 ) ^ { 3 } \times 27 \times t ^ { 4 } } { ( 3 ) ^ { 2 } \times ( 3 ) ^ { 4 } \times t ^ { 2 } }$$

Aromātai

$$27t^{2}$$

Ngā Upane Otinga

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 2 me te 4 kia riro ai te 6.

$$\frac{9^{3}\times 27t^{4}}{3^{6}t^{2}}$$

Me whakakore tahi te t^{2} i te taurunga me te tauraro.

$$\frac{27\times 9^{3}t^{2}}{3^{6}}$$

Tātaihia te 9 mā te pū o 3, kia riro ko 729.

$$\frac{27\times 729t^{2}}{3^{6}}$$

Whakareatia te 27 ki te 729, ka 19683.

$$\frac{19683t^{2}}{3^{6}}$$

Tātaihia te 3 mā te pū o 6, kia riro ko 729.

$$\frac{19683t^{2}}{729}$$

Whakawehea te 19683t^{2} ki te 729, kia riro ko 27t^{2}.

$$27t^{2}$$

Kimi Pārōnaki e ai ki t

$$54t$$

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.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{19683}{729}t^{4-2})$$

Mahia ngā tātaitanga.

$$\frac{\mathrm{d}}{\mathrm{d}t}(27t^{2})$$

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}.

$$2\times 27t^{2-1}$$

Mahia ngā tātaitanga.

$$54t^{1}$$

Mō tētahi kupu t, t^{1}=t.

$$54t$$