Whakaoti i te d/dxx^2(2+x)/x^2-x

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

Aromātai

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

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}\left(2+x\right)}{x^{2}-x}.

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

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

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

Whakamahia te āhuatanga tohatoha hei whakarea te x ki te x+2.

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

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.

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

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}.

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

Whakarūnātia.

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

Whakareatia x^{1}-1 ki te 2x^{1}+2x^{0}.

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

Whakareatia x^{2}+2x^{1} ki te x^{0}.

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

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

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

Whakarūnātia.

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

Pahekotia ngā kīanga tau ōrite.

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

Mō tētahi kupu t, t^{1}=t.

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

Mō tētahi kupu t mahue te 0, t^{0}=1.

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

Kimi Pārōnaki e ai ki x

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