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Kimi Pārōnaki e ai ki z
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Tohaina

\left(\frac{1}{z}\right)^{2}
Whakamahia ngā ture taupū hei whakarūnā i te kīanga.
z^{-2}
Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū.
\frac{1}{z^{2}}
Whakareatia -1 ki te 2.
\left(\frac{1}{z^{1}}\right)^{2}
Whakamahia ngā ture taupū hei whakarūnā i te kīanga.
\frac{1^{2}}{\left(z^{1}\right)^{2}}
Hei hiki i te otinga o ngā tau e rua ki tētahi pū, hīkina ia tau ki te pū ka whakawehe.
\frac{1}{z^{2}}
Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū.
2\times \left(\frac{1}{z}\right)^{2-1}\frac{\mathrm{d}}{\mathrm{d}z}(\frac{1}{z})
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).
2\times \left(\frac{1}{z}\right)^{1}\left(-1\right)z^{-1-1}
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}.
-2z^{-2}\times \left(\frac{1}{z}\right)^{1}
Whakarūnātia.
-2z^{-2}\times \frac{1}{z}
Mō tētahi kupu t, t^{1}=t.