Whakaoti i te frac{10^{5}x6^5x24}{48^2x15^4x4^3}

$$\frac { 10 ^ { 5 } x 6 ^ { 5 } x 24 } { 48 ^ { 2 } x 15 ^ { 4 } x 4 ^ { 3 } }$$

Aromātai

$$\frac{5x_{24}}{48x}$$

Ngā Upane Otinga

Whakareatia te x ki te x, ka x^{2}.

$$\frac{10^{5}x\times 6^{5}x_{24}}{48^{2}x^{2}\times 15^{4}\times 4^{3}}$$

Me whakakore tahi te x i te taurunga me te tauraro.

$$\frac{6^{5}\times 10^{5}x_{24}}{4^{3}\times 15^{4}\times 48^{2}x}$$

Tātaihia te 6 mā te pū o 5, kia riro ko 7776.

$$\frac{7776\times 10^{5}x_{24}}{4^{3}\times 15^{4}\times 48^{2}x}$$

Tātaihia te 10 mā te pū o 5, kia riro ko 100000.

$$\frac{7776\times 100000x_{24}}{4^{3}\times 15^{4}\times 48^{2}x}$$

Whakareatia te 7776 ki te 100000, ka 777600000.

$$\frac{777600000x_{24}}{4^{3}\times 15^{4}\times 48^{2}x}$$

Tātaihia te 4 mā te pū o 3, kia riro ko 64.

$$\frac{777600000x_{24}}{64\times 15^{4}\times 48^{2}x}$$

Tātaihia te 15 mā te pū o 4, kia riro ko 50625.

$$\frac{777600000x_{24}}{64\times 50625\times 48^{2}x}$$

Whakareatia te 64 ki te 50625, ka 3240000.

$$\frac{777600000x_{24}}{3240000\times 48^{2}x}$$

Tātaihia te 48 mā te pū o 2, kia riro ko 2304.

$$\frac{777600000x_{24}}{3240000\times 2304x}$$

Whakareatia te 3240000 ki te 2304, ka 7464960000.

$$\frac{777600000x_{24}}{7464960000x}$$

Me whakakore tahi te 155520000 i te taurunga me te tauraro.

$$\frac{5x_{24}}{48x}$$

Kimi Pārōnaki e ai ki x

$$-\frac{5x_{24}}{48x^{2}}$$

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.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{777600000x_{24}}{7464960000x}x^{1-1})$$

Mahia ngā tātaitanga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x_{24}}{48x}x^{0})$$

Mō tētahi tau a mahue te 0, a^{0}=1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5x_{24}}{48x})$$

Ko te pārōnaki o tētahi kupu taimau ko te 0.

$$0$$