Whakaoti i te (9x^2arctan(3x-1)/6(9x^2-6x+2))^prime

$$( \frac { 9 x ^ { 2 } \arctan ( 3 x - 1 ) } { 6 ( 9 x ^ { 2 } - 6 x + 2 ) } ) ^ { \prime }$$

Aromātai

$$\frac{3x\left(-6x\arctan(3x-1)+4\arctan(3x-1)+3x\right)}{2\left(9x^{2}-6x+2\right)^{2}}$$

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

Me whakakore tahi te 3 i te taurunga me te tauraro.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x^{2}\arctan(3x-1)}{2\left(9x^{2}-6x+2\right)})$$

Whakamahia te āhuatanga tohatoha hei whakarea te 2 ki te 9x^{2}-6x+2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x^{2}\arctan(3x-1)}{18x^{2}-12x+4})$$

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.

$$\frac{\left(18x^{2}-12x^{1}+4\right)\frac{\mathrm{d}}{\mathrm{d}x}(3\arctan(3x-1)x^{2})-3\arctan(3x-1)x^{2}\frac{\mathrm{d}}{\mathrm{d}x}(18x^{2}-12x^{1}+4)}{\left(18x^{2}-12x^{1}+4\right)^{2}}$$

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}.

$$\frac{\left(18x^{2}-12x^{1}+4\right)\times 2\times 3\arctan(3x-1)x^{2-1}-3\arctan(3x-1)x^{2}\left(2\times 18x^{2-1}-12x^{1-1}\right)}{\left(18x^{2}-12x^{1}+4\right)^{2}}$$

Whakarūnātia.

$$\frac{\left(18x^{2}-12x^{1}+4\right)\times 6\arctan(3x-1)x^{1}-3\arctan(3x-1)x^{2}\left(36x^{1}-12x^{0}\right)}{\left(18x^{2}-12x^{1}+4\right)^{2}}$$

Whakareatia 18x^{2}-12x^{1}+4 ki te 6\arctan(3x-1)x^{1}.

$$\frac{18x^{2}\times 6\arctan(3x-1)x^{1}-12x^{1}\times 6\arctan(3x-1)x^{1}+4\times 6\arctan(3x-1)x^{1}-3\arctan(3x-1)x^{2}\left(36x^{1}-12x^{0}\right)}{\left(18x^{2}-12x^{1}+4\right)^{2}}$$

Whakareatia 3\arctan(3x-1)x^{2} ki te 36x^{1}-12x^{0}.

$$\frac{18x^{2}\times 6\arctan(3x-1)x^{1}-12x^{1}\times 6\arctan(3x-1)x^{1}+4\times 6\arctan(3x-1)x^{1}-\left(3\arctan(3x-1)x^{2}\times 36x^{1}+3\arctan(3x-1)x^{2}\left(-12\right)x^{0}\right)}{\left(18x^{2}-12x^{1}+4\right)^{2}}$$

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

$$\frac{18\times 6\arctan(3x-1)x^{2+1}-12\times 6\arctan(3x-1)x^{1+1}+4\times 6\arctan(3x-1)x^{1}-\left(3\arctan(3x-1)\times 36x^{2+1}+3\arctan(3x-1)\left(-12\right)x^{2}\right)}{\left(18x^{2}-12x^{1}+4\right)^{2}}$$

Whakarūnātia.

$$\frac{108\arctan(3x-1)x^{3}+\left(-72\arctan(3x-1)\right)x^{2}+24\arctan(3x-1)x^{1}-\left(108\arctan(3x-1)x^{3}+\left(-36\arctan(3x-1)\right)x^{2}\right)}{\left(18x^{2}-12x^{1}+4\right)^{2}}$$

Pahekotia ngā kīanga tau ōrite.

$$\frac{\left(-36\arctan(3x-1)\right)x^{2}+24\arctan(3x-1)x^{1}}{\left(18x^{2}-12x^{1}+4\right)^{2}}$$

Mō tētahi kupu t, t^{1}=t.

$$\frac{\left(-36\arctan(3x-1)\right)x^{2}+24\arctan(3x-1)x}{\left(18x^{2}-12x+4\right)^{2}}$$

Kimi Pārōnaki e ai ki x

$$\frac{3\left(54x^{3}\arctan(3x-1)-54x^{2}\arctan(3x-1)+4\arctan(3x-1)-27x^{3}-9x^{2}+12x\right)}{\left(9x^{2}-6x+2\right)^{3}}$$