Whakaoti i te d/dxleft(2x^2+10000x/x^2right)

$$\frac{d}{d x } \left(2 { x }^{ 2 } + \frac{ 10000x }{ { x }^{ 2 } } \right)$$

Aromātai

$$4x-\frac{10000}{x^{2}}$$

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}+\frac{10000}{x})$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 2x^{2} ki te \frac{x}{x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{2}x}{x}+\frac{10000}{x})$$

Tā te mea he rite te tauraro o \frac{2x^{2}x}{x} me \frac{10000}{x}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{2}x+10000}{x})$$

Mahia ngā whakarea i roto o 2x^{2}x+10000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{3}+10000}{x})$$

Mo ētahi pānga e rua e taea ana te pārōnaki, ko te pārōnaki o te hua o ngā pānga e rua ko te pānga tuatahi whakareatia ki te pārōnaki o te pānga tuarua tāpiri i te pānga tuarua whakareatia ki te pārōnaki o te mea tuatahi.

$$\left(2x^{3}+10000\right)\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{x})+\frac{1}{x}\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+10000)$$

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}.

$$\left(2x^{3}+10000\right)\left(-1\right)x^{-1-1}+\frac{1}{x}\times 3\times 2x^{3-1}$$

Whakarūnātia.

$$\left(2x^{3}+10000\right)\left(-1\right)x^{-2}+\frac{1}{x}\times 6x^{2}$$

Whakareatia 2x^{3}+10000 ki te -x^{-2}.

$$2x^{3}\left(-1\right)x^{-2}+10000\left(-1\right)x^{-2}+\frac{1}{x}\times 6x^{2}$$

Hei whakarea pū o te pūtake ōrite, tāpiri ana taupū.

$$-2x^{3-2}-10000x^{-2}+6x^{-1+2}$$

Whakarūnātia.

$$-2x^{1}-10000x^{-2}+6x^{1}$$

Mō tētahi kupu t, t^{1}=t.

$$-2x-10000x^{-2}+6x$$

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

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{2}+\frac{10000}{x})$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Whakareatia 2x^{2} ki te \frac{x}{x}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{2}x}{x}+\frac{10000}{x})$$

Tā te mea he rite te tauraro o \frac{2x^{2}x}{x} me \frac{10000}{x}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{2}x+10000}{x})$$

Mahia ngā whakarea i roto o 2x^{2}x+10000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2x^{3}+10000}{x})$$

Mō ngā pānga e rua e taea ana te pārōnaki, ko te pārōnaki o te otinga o ngā pānga e rua ko te tauraro whakareatia ki te pārōnaki o te taurunga tango i te taurunga whakareatia ki te pārōnaki o te tauraro, ā, ka whakawehea te katoa ki te tauraro kua pūruatia.

$$\frac{x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(2x^{3}+10000)-\left(2x^{3}+10000\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1})}{\left(x^{1}\right)^{2}}$$

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}.

$$\frac{x^{1}\times 3\times 2x^{3-1}-\left(2x^{3}+10000\right)x^{1-1}}{\left(x^{1}\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{x^{1}\times 6x^{2}-\left(2x^{3}+10000\right)x^{0}}{\left(x^{1}\right)^{2}}$$

Whakarohaina mā te āhuatanga tohatoha.

$$\frac{x^{1}\times 6x^{2}-\left(2x^{3}x^{0}+10000x^{0}\right)}{\left(x^{1}\right)^{2}}$$

Hei whakarea pū o te pūtake ōrite, tāpiri ana taupū.

$$\frac{6x^{1+2}-\left(2x^{3}+10000x^{0}\right)}{\left(x^{1}\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{6x^{3}-\left(2x^{3}+10000x^{0}\right)}{\left(x^{1}\right)^{2}}$$

Tangohia ngā taiapa kāore i te hiahiatia.

$$\frac{6x^{3}-2x^{3}-10000x^{0}}{\left(x^{1}\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{\left(6-2\right)x^{3}-10000x^{0}}{\left(x^{1}\right)^{2}}$$

Tango 2 mai i 6.

$$\frac{4x^{3}-10000x^{0}}{\left(x^{1}\right)^{2}}$$

Tauwehea te 4.

$$\frac{4\left(x^{3}-2500x^{0}\right)}{\left(x^{1}\right)^{2}}$$

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.

$$\frac{4\left(x^{3}-2500x^{0}\right)}{1^{2}x^{2}}$$

Hīkina te 1 ki te pū 2.

$$\frac{4\left(x^{3}-2500x^{0}\right)}{x^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{4\left(x^{3}-2500\times 1\right)}{x^{2}}$$

Mō tētahi kupu t, t\times 1=t me 1t=t.

$$\frac{4\left(x^{3}-2500\right)}{x^{2}}$$

Kimi Pārōnaki e ai ki x

$$4+\frac{20000}{x^{3}}$$