Whakaoti i te (u^2)^6(u^5)^6

$$( u ^ { 2 } ) ^ { 6 } ( u ^ { 5 } ) ^ { 6 }$$

Aromātai

$$u^{42}$$

Ngā Upane mō te Hua o ngā Pānga Taupū e Rua

Whakamahia ngā ture taupū hei whakarūnā i te kīanga.

$$\left(u^{2}\right)^{6}\left(u^{5}\right)^{6}$$

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

$$u^{2\times 6}u^{5\times 6}$$

Whakareatia 2 ki te 6.

$$u^{12}u^{5\times 6}$$

Whakareatia 5 ki te 6.

$$u^{12}u^{30}$$

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

$$u^{12+30}$$

Tāpirihia ngā taupū 12 me 30.

$$u^{42}$$

Kimi Pārōnaki e ai ki u

$$42u^{41}$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Pārōnaki

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 2 me te 6 kia riro ai te 12.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{12}\left(u^{5}\right)^{6})$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 5 me te 6 kia riro ai te 30.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{12}u^{30})$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 12 me te 30 kia riro ai te 42.

$$\frac{\mathrm{d}}{\mathrm{d}u}(u^{42})$$

Ko te pārōnaki o ax^{n} ko nax^{n-1}.

$$42u^{42-1}$$

Tango 1 mai i 42.

$$42u^{41}$$