Whakaoti i te [2x/1+x^2]^prime

$$[ \frac { 2 x } { 1 + x ^ { 2 } } ] ^ { \prime }$$

Aromātai

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

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.

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

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}.

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

Mahia ngā tātaitanga.

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

Whakarohaina mā te āhuatanga tohatoha.

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

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

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

Mahia ngā tātaitanga.

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

Pahekotia ngā kīanga tau ōrite.

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

Tango 4 mai i 2.

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

Tauwehea te 2.

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

Mō tētahi kupu t mahue te 0, t^{0}=1.

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

Kimi Pārōnaki e ai ki x

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