Aromātai
\frac{z^{3}}{4}
Kimi Pārōnaki e ai ki z
\frac{3z^{2}}{4}
Tohaina
Kua tāruatia ki te papatopenga
\frac{1}{4z^{-3}}
Whakamahia ngā ture taupū hei whakarūnā i te kīanga.
\frac{1}{4}\times \frac{1}{z^{-3}}
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.
\frac{1}{4}z^{-3\left(-1\right)}
Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū.
\frac{1}{4}z^{3}
Whakareatia -3 ki te -1.
-\left(4z^{-3}\right)^{-1-1}\frac{\mathrm{d}}{\mathrm{d}z}(4z^{-3})
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(4z^{-3}\right)^{-2}\left(-3\right)\times 4z^{-3-1}
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}.
12z^{-4}\times \left(4z^{-3}\right)^{-2}
Whakarūnātia.
Ngā Tauira
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{ x } ^ { 2 } - 4 x - 5 = 0
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