Whakaoti i te d/dxleft(x^2-x/x^3-x^2-x+1right)

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

Aromātai

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

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

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{x^{2}-x}{x^{3}-x^{2}-x+1}.

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

Me whakakore tahi te x-1 i te taurunga me te tauraro.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{\left(x-1\right)\left(x+1\right)})$$

Whakaarohia te \left(x-1\right)\left(x+1\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}. Pūrua 1.

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

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.

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

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}.

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

Mahia ngā tātaitanga.

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

Whakarohaina mā te āhuatanga tohatoha.

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

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

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

Mahia ngā tātaitanga.

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

Pahekotia ngā kīanga tau ōrite.

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

Tango 2 mai i 1.

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

Mō tētahi kupu t mahue te 0, t^{0}=1.

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

Kimi Pārōnaki e ai ki x

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