Whakaoti i te (a^-7diva^15)div(a^6)^4

$$( a ^ { - 7 } \div a ^ { 15 } ) \div ( a ^ { 6 } ) ^ { 4 }$$

Aromātai

$$\frac{1}{a^{46}}$$

Ngā Upane Otinga

Tuhia anō te a^{15} hei a^{-7}a^{22}. Me whakakore tahi te a^{-7} i te taurunga me te tauraro.

$$\frac{\frac{1}{a^{22}}}{\left(a^{6}\right)^{4}}$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 6 me te 4 kia riro ai te 24.

$$\frac{\frac{1}{a^{22}}}{a^{24}}$$

Tuhia te \frac{\frac{1}{a^{22}}}{a^{24}} hei hautanga kotahi.

$$\frac{1}{a^{22}a^{24}}$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 22 me te 24 kia riro ai te 46.

$$\frac{1}{a^{46}}$$

Kimi Pārōnaki e ai ki a

$$-\frac{46}{a^{47}}$$

Ngā Upane e Whakamahi ana i te Ture Mekameka

Tuhia anō te a^{15} hei a^{-7}a^{22}. Me whakakore tahi te a^{-7} i te taurunga me te tauraro.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{1}{a^{22}}}{\left(a^{6}\right)^{4}})$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 6 me te 4 kia riro ai te 24.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{\frac{1}{a^{22}}}{a^{24}})$$

Tuhia te \frac{\frac{1}{a^{22}}}{a^{24}} hei hautanga kotahi.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{a^{22}a^{24}})$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 22 me te 24 kia riro ai te 46.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{1}{a^{46}})$$

Mēnā ko F te hanganga o ngā pānga e rua e taea ana te pārōnaki f\left(u\right) me u=g\left(x\right), arā, mēnā ko F\left(x\right)=f\left(g\left(x\right)\right), ko te pārōnaki o F te pārōnaki o f e ai ki u whakareatia te pārōnaki o g e ai ki x, arā, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

$$-\left(a^{46}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}a}(a^{46})$$

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}.

$$-\left(a^{46}\right)^{-2}\times 46a^{46-1}$$

Whakarūnātia.

$$-46a^{45}\left(a^{46}\right)^{-2}$$