Whakaoti i te d/dxleft(3x^2-2/x-5right)2

$$\frac{d}{d x } \left( \frac{ 3 { x }^{ 2 } -2 }{ x-5 } \right) 2$$

Aromātai

$$\frac{2\left(3x^{2}-30x+2\right)}{\left(x-5\right)^{2}}$$

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

Tuhia te \frac{3x^{2}-2}{x-5}\times 2 hei hautanga kotahi.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\left(3x^{2}-2\right)\times 2}{x-5})$$

Whakamahia te āhuatanga tohatoha hei whakarea te 3x^{2}-2 ki te 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{6x^{2}-4}{x-5})$$

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.

$$\frac{\left(x^{1}-5\right)\frac{\mathrm{d}}{\mathrm{d}x}(6x^{2}-4)-\left(6x^{2}-4\right)\frac{\mathrm{d}}{\mathrm{d}x}(x^{1}-5)}{\left(x^{1}-5\right)^{2}}$$

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}.

$$\frac{\left(x^{1}-5\right)\times 2\times 6x^{2-1}-\left(6x^{2}-4\right)x^{1-1}}{\left(x^{1}-5\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{\left(x^{1}-5\right)\times 12x^{1}-\left(6x^{2}-4\right)x^{0}}{\left(x^{1}-5\right)^{2}}$$

Whakarohaina mā te āhuatanga tohatoha.

$$\frac{x^{1}\times 12x^{1}-5\times 12x^{1}-\left(6x^{2}x^{0}-4x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

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

$$\frac{12x^{1+1}-5\times 12x^{1}-\left(6x^{2}-4x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{12x^{2}-60x^{1}-\left(6x^{2}-4x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

Tangohia ngā taiapa kāore i te hiahiatia.

$$\frac{12x^{2}-60x^{1}-6x^{2}-\left(-4x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{\left(12-6\right)x^{2}-60x^{1}-\left(-4x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

Tango 6 mai i 12.

$$\frac{6x^{2}-60x^{1}-\left(-4x^{0}\right)}{\left(x^{1}-5\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{6x^{2}-60x-\left(-4x^{0}\right)}{\left(x-5\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{6x^{2}-60x-\left(-4\right)}{\left(x-5\right)^{2}}$$

Kimi Pārōnaki e ai ki x

$$\frac{292}{\left(x-5\right)^{3}}$$