Whakaoti i te 4x^1/2/8x^1/3

$$\frac { 4 x ^ { 1 / 2 } } { 8 x ^ { 1 / 3 } }$$

Aromātai

$$\frac{\sqrt[6]{x}}{2}$$

Ngā Upane mō te Otinga o ngā Pānga Taupū

Whakamahia ngā ture taupū hei whakarūnā i te kīanga.

$$\frac{4^{1}\sqrt{x}}{8^{1}\sqrt[3]{x}}$$

Hei whakawehe i ngā pū o te pūtake kotahi, tangohia te taupū o te tauraro mai i te taupū o te taurunga.

$$\frac{4^{1}x^{\frac{1}{2}-\frac{1}{3}}}{8^{1}}$$

Tango \frac{1}{3} mai i \frac{1}{2} mā te kimi i te tauraro pātahi me te tango i ngā taurunga, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$\frac{4^{1}\sqrt[6]{x}}{8^{1}}$$

Whakahekea te hautanga \frac{4}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{1}{2}\sqrt[6]{x}$$

Kimi Pārōnaki e ai ki x

$$\frac{1}{12x^{\frac{5}{6}}}$$

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.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4}{8}x^{\frac{1}{2}-\frac{1}{3}})$$

Mahia ngā tātaitanga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{2}\sqrt[6]{x})$$

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}.

$$\frac{1}{6}\times \frac{1}{2}x^{\frac{1}{6}-1}$$

Mahia ngā tātaitanga.

$$\frac{1}{12}x^{-\frac{5}{6}}$$