Whakaoti i te 3/2x*(x^2/6x+10)

$$\frac{ 3 }{ 2x } \times ( \frac{ { x }^{ 2 } }{ 6x+10 } )$$

Aromātai

$$\frac{3x}{4\left(3x+5\right)}$$

Ngā Hipanga Rongoā Poto

Me whakarea te \frac{3}{2x} ki te \frac{x^{2}}{6x+10} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{3x^{2}}{2x\left(6x+10\right)}$$

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

$$\frac{3x}{2\left(6x+10\right)}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te 6x+10.

$$\frac{3x}{12x+20}$$

Kimi Pārōnaki e ai ki x

$$\frac{15}{4\left(3x+5\right)^{2}}$$

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

Me whakarea te \frac{3}{2x} ki te \frac{x^{2}}{6x+10} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x^{2}}{2x\left(6x+10\right)})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x}{2\left(6x+10\right)})$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te 6x+10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x}{12x+20})$$

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.

$$\frac{\left(12x^{1}+20\right)\frac{\mathrm{d}}{\mathrm{d}x}(3x^{1})-3x^{1}\frac{\mathrm{d}}{\mathrm{d}x}(12x^{1}+20)}{\left(12x^{1}+20\right)^{2}}$$

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}.

$$\frac{\left(12x^{1}+20\right)\times 3x^{1-1}-3x^{1}\times 12x^{1-1}}{\left(12x^{1}+20\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{\left(12x^{1}+20\right)\times 3x^{0}-3x^{1}\times 12x^{0}}{\left(12x^{1}+20\right)^{2}}$$

Whakarohaina mā te āhuatanga tohatoha.

$$\frac{12x^{1}\times 3x^{0}+20\times 3x^{0}-3x^{1}\times 12x^{0}}{\left(12x^{1}+20\right)^{2}}$$

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

$$\frac{12\times 3x^{1}+20\times 3x^{0}-3\times 12x^{1}}{\left(12x^{1}+20\right)^{2}}$$

Mahia ngā tātaitanga.

$$\frac{36x^{1}+60x^{0}-36x^{1}}{\left(12x^{1}+20\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{\left(36-36\right)x^{1}+60x^{0}}{\left(12x^{1}+20\right)^{2}}$$

Tango 36 mai i 36.

$$\frac{60x^{0}}{\left(12x^{1}+20\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{60x^{0}}{\left(12x+20\right)^{2}}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{60\times 1}{\left(12x+20\right)^{2}}$$

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

$$\frac{60}{\left(12x+20\right)^{2}}$$