Whakaoti i te x^199/x^200+100

$$\frac { x ^ { 199 } } { x ^ { 200 } + 100 }$$

Kimi Pārōnaki e ai ki x

$$\frac{x^{198}\left(19900-x^{200}\right)}{\left(x^{200}+100\right)^{2}}$$

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

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.

$$\frac{\left(x^{200}+100\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{199})-x^{199}\frac{\mathrm{d}}{\mathrm{d}x}(x^{200}+100)}{\left(x^{200}+100\right)^{2}}$$

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}.

$$\frac{\left(x^{200}+100\right)\times 199x^{199-1}-x^{199}\times 200x^{200-1}}{\left(x^{200}+100\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{\left(x^{200}+100\right)\times 199x^{198}-x^{199}\times 200x^{199}}{\left(x^{200}+100\right)^{2}}$$

Whakarohaina mā te āhuatanga tohatoha.

$$\frac{x^{200}\times 199x^{198}+100\times 199x^{198}-x^{199}\times 200x^{199}}{\left(x^{200}+100\right)^{2}}$$

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

$$\frac{199x^{200+198}+100\times 199x^{198}-200x^{199+199}}{\left(x^{200}+100\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{199x^{398}+19900x^{198}-200x^{398}}{\left(x^{200}+100\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{\left(199-200\right)x^{398}+19900x^{198}}{\left(x^{200}+100\right)^{2}}$$

Tango 200 mai i 199.

$$\frac{-x^{398}+19900x^{198}}{\left(x^{200}+100\right)^{2}}$$

Tauwehea te x^{198}.

$$\frac{x^{198}\left(-x^{200}+19900x^{0}\right)}{\left(x^{200}+100\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{x^{198}\left(-x^{200}+19900\times 1\right)}{\left(x^{200}+100\right)^{2}}$$

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

$$\frac{x^{198}\left(-x^{200}+19900\right)}{\left(x^{200}+100\right)^{2}}$$

Aromātai

$$\frac{x^{199}}{x^{200}+100}$$