Whakaoti i te w/w-frac{w{y}}

$$\frac { w } { w - \frac { w } { y } }$$

Aromātai

$$\frac{y}{y-1}$$

Ngā Hipanga Rongoā Poto

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

$$\frac{w}{\frac{wy}{y}-\frac{w}{y}}$$

Tā te mea he rite te tauraro o \frac{wy}{y} me \frac{w}{y}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{w}{\frac{wy-w}{y}}$$

Whakawehe w ki te \frac{wy-w}{y} mā te whakarea w ki te tau huripoki o \frac{wy-w}{y}.

$$\frac{wy}{wy-w}$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea.

$$\frac{wy}{w\left(y-1\right)}$$

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

$$\frac{y}{y-1}$$

Kimi Pārōnaki e ai ki y

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

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. Whakareatia w ki te \frac{y}{y}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{w}{\frac{wy}{y}-\frac{w}{y}})$$

Tā te mea he rite te tauraro o \frac{wy}{y} me \frac{w}{y}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{w}{\frac{wy-w}{y}})$$

Whakawehe w ki te \frac{wy-w}{y} mā te whakarea w ki te tau huripoki o \frac{wy-w}{y}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{wy}{wy-w})$$

Me whakatauwehe ngā kīanga kāore anō i whakatauwehea i roto o \frac{wy}{wy-w}.

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{wy}{w\left(y-1\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}y}(\frac{y}{y-1})$$

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.

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

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}.

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

Mahia ngā tātaitanga.

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

Whakarohaina mā te āhuatanga tohatoha.

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

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

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

Pahekotia ngā kīanga tau ōrite.

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

Tango 1 mai i 1.

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

Mō tētahi kupu t, t^{1}=t.

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

Mō tētahi kupu t mahue te 0, t^{0}=1.

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