Whakaoti i te d/dx(8x^6-9x^10)(8x^6+9x^10)

$$\frac { d } { d x } ( 8 x ^ { 6 } - 9 x ^ { 10 } ) ( 8 x ^ { 6 } + 9 x ^ { 10 } )$$

Aromātai

$$768x^{11}-1620x^{19}$$

Ngā Upane e Whakamahi ana i te Ture Pārōnaki mō te Tapeke

Whakaarohia te \left(8x^{6}-9x^{10}\right)\left(8x^{6}+9x^{10}\right). Ka taea te whakareanga te panoni ki te rerekētanga o ngā pūrua mā te ture: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(8x^{6}\right)^{2}-\left(9x^{10}\right)^{2})$$

Whakarohaina te \left(8x^{6}\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8^{2}\left(x^{6}\right)^{2}-\left(9x^{10}\right)^{2})$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 6 me te 2 kia riro ai te 12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8^{2}x^{12}-\left(9x^{10}\right)^{2})$$

Tātaihia te 8 mā te pū o 2, kia riro ko 64.

$$\frac{\mathrm{d}}{\mathrm{d}x}(64x^{12}-\left(9x^{10}\right)^{2})$$

Whakarohaina te \left(9x^{10}\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(64x^{12}-9^{2}\left(x^{10}\right)^{2})$$

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū. Me whakarea te 10 me te 2 kia riro ai te 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(64x^{12}-9^{2}x^{20})$$

Tātaihia te 9 mā te pū o 2, kia riro ko 81.

$$\frac{\mathrm{d}}{\mathrm{d}x}(64x^{12}-81x^{20})$$

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}.

$$12\times 64x^{12-1}+20\left(-81\right)x^{20-1}$$

Whakareatia 12 ki te 64.

$$768x^{12-1}+20\left(-81\right)x^{20-1}$$

Tango 1 mai i 12.

$$768x^{11}+20\left(-81\right)x^{20-1}$$

Whakareatia 20 ki te -81.

$$768x^{11}-1620x^{20-1}$$

Tango 1 mai i 20.

$$768x^{11}-1620x^{19}$$

Kimi Pārōnaki e ai ki x

$$8448x^{10}-30780x^{18}$$