Whakaoti i te x_{1}(sqrt{1/3}+sqrt{27})*sqrt{3}

$$x _ { 1 } ( \sqrt { \frac { 1 } { 3 } } + \sqrt { 27 } ) \times \sqrt { 3 }$$

Aromātai

$$10x_{1}$$

Ngā Upane Otinga

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1}{3}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{3}}.

$$x_{1}\left(\frac{\sqrt{1}}{\sqrt{3}}+\sqrt{27}\right)\sqrt{3}$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$x_{1}\left(\frac{1}{\sqrt{3}}+\sqrt{27}\right)\sqrt{3}$$

Whakangāwaritia te tauraro o \frac{1}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$x_{1}\left(\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\sqrt{27}\right)\sqrt{3}$$

Ko te pūrua o \sqrt{3} ko 3.

$$x_{1}\left(\frac{\sqrt{3}}{3}+\sqrt{27}\right)\sqrt{3}$$

Tauwehea te 27=3^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 3} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{3}. Tuhia te pūtakerua o te 3^{2}.

$$x_{1}\left(\frac{\sqrt{3}}{3}+3\sqrt{3}\right)\sqrt{3}$$

Pahekotia te \frac{\sqrt{3}}{3} me 3\sqrt{3}, ka \frac{10}{3}\sqrt{3}.

$$x_{1}\times \frac{10}{3}\sqrt{3}\sqrt{3}$$

Whakareatia te \sqrt{3} ki te \sqrt{3}, ka 3.

$$x_{1}\times \frac{10}{3}\times 3$$

Me whakakore te 3 me te 3.

$$x_{1}\times 10$$

Kimi Pārōnaki e ai ki x_1

$$10$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Pārōnaki

Tuhia anō te pūtake rua o te whakawehenga \sqrt{\frac{1}{3}} hei whakawehenga o ngā pūtake rua \frac{\sqrt{1}}{\sqrt{3}}.

$$\frac{\mathrm{d}}{\mathrm{d}x_{1}}(x_{1}\left(\frac{\sqrt{1}}{\sqrt{3}}+\sqrt{27}\right)\sqrt{3})$$

Tātaitia te pūtakerua o 1 kia tae ki 1.

$$\frac{\mathrm{d}}{\mathrm{d}x_{1}}(x_{1}\left(\frac{1}{\sqrt{3}}+\sqrt{27}\right)\sqrt{3})$$

Whakangāwaritia te tauraro o \frac{1}{\sqrt{3}} mā te whakarea i te taurunga me te tauraro ki te \sqrt{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x_{1}}(x_{1}\left(\frac{\sqrt{3}}{\left(\sqrt{3}\right)^{2}}+\sqrt{27}\right)\sqrt{3})$$

Ko te pūrua o \sqrt{3} ko 3.

$$\frac{\mathrm{d}}{\mathrm{d}x_{1}}(x_{1}\left(\frac{\sqrt{3}}{3}+\sqrt{27}\right)\sqrt{3})$$

Tauwehea te 27=3^{2}\times 3. Tuhia anō te pūtake rua o te hua \sqrt{3^{2}\times 3} hei hua o ngā pūtake rua \sqrt{3^{2}}\sqrt{3}. Tuhia te pūtakerua o te 3^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x_{1}}(x_{1}\left(\frac{\sqrt{3}}{3}+3\sqrt{3}\right)\sqrt{3})$$

Pahekotia te \frac{\sqrt{3}}{3} me 3\sqrt{3}, ka \frac{10}{3}\sqrt{3}.

$$\frac{\mathrm{d}}{\mathrm{d}x_{1}}(x_{1}\times \frac{10}{3}\sqrt{3}\sqrt{3})$$

Whakareatia te \sqrt{3} ki te \sqrt{3}, ka 3.

$$\frac{\mathrm{d}}{\mathrm{d}x_{1}}(x_{1}\times \frac{10}{3}\times 3)$$

Me whakakore te 3 me te 3.

$$\frac{\mathrm{d}}{\mathrm{d}x_{1}}(x_{1}\times 10)$$

Ko te pārōnaki o ax^{n} ko nax^{n-1}.

$$10x_{1}^{1-1}$$

Tango 1 mai i 1.

$$10x_{1}^{0}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$10\times 1$$

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

$$10$$