Whakaoti i te d/dx(2/x-3/x^2)=

$$\frac { d } { d x } ( \frac { 2 } { x } - \frac { 3 } { x ^ { 2 } } ) =$$

Aromātai

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

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

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o x me x^{2} ko x^{2}. Whakareatia \frac{2}{x} ki te \frac{x}{x}.

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

Tā te mea he rite te tauraro o \frac{2x}{x^{2}} me \frac{3}{x^{2}}, me tango rāua mā te tango i ō raua taurunga.

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

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.

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

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}.

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

Mahia ngā tātaitanga.

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

Whakarohaina mā te āhuatanga tohatoha.

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

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

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

Mahia ngā tātaitanga.

$$\frac{2x^{2}-\left(4x^{2}-6x^{1}\right)}{\left(x^{2}\right)^{2}}$$

Tangohia ngā taiapa kāore i te hiahiatia.

$$\frac{2x^{2}-4x^{2}-\left(-6x^{1}\right)}{\left(x^{2}\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{\left(2-4\right)x^{2}-\left(-6x^{1}\right)}{\left(x^{2}\right)^{2}}$$

Tango 4 mai i 2.

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

Tauwehea te 2x.

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

Hei hiki pū ki tētahi pū anō, me whakarea ngā taupū.

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

Whakareatia 2 ki te 2.

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

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

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

Tango 1 mai i 4.

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

Mō tētahi kupu t, t^{1}=t.

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

Mō tētahi kupu t mahue te 0, t^{0}=1.

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

Kimi Pārōnaki e ai ki x

$$\frac{2\left(2x-9\right)}{x^{4}}$$