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\frac{x^{4}x^{3}}{x\times \frac{1}{2}xx\times \frac{1}{2}}\times \frac{x\times \frac{1}{2}xx\times \frac{1}{2}}{x^{2}xx^{3}}
Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 3 me te 1 kia riro ai te 4.
\frac{x^{7}}{x\times \frac{1}{2}xx\times \frac{1}{2}}\times \frac{x\times \frac{1}{2}xx\times \frac{1}{2}}{x^{2}xx^{3}}
Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 4 me te 3 kia riro ai te 7.
\frac{x^{7}}{x^{2}\times \frac{1}{2}x\times \frac{1}{2}}\times \frac{x\times \frac{1}{2}xx\times \frac{1}{2}}{x^{2}xx^{3}}
Whakareatia te x ki te x, ka x^{2}.
\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x\times \frac{1}{2}xx\times \frac{1}{2}}{x^{2}xx^{3}}
Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 2 me te 1 kia riro ai te 3.
\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x^{2}\times \frac{1}{2}x\times \frac{1}{2}}{x^{2}xx^{3}}
Whakareatia te x ki te x, ka x^{2}.
\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{2}xx^{3}}
Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 2 me te 1 kia riro ai te 3.
\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{3}x^{3}}
Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 2 me te 1 kia riro ai te 3.
\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{6}}
Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 3 me te 3 kia riro ai te 6.
\frac{x^{4}}{\frac{1}{2}\times \frac{1}{2}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{6}}
Me whakakore tahi te x^{3} i te taurunga me te tauraro.
\frac{x^{4}}{\frac{1}{4}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{6}}
Whakareatia te \frac{1}{2} ki te \frac{1}{2}, ka \frac{1}{4}.
x^{4}\times 4\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{6}}
Whakawehe x^{4} ki te \frac{1}{4} mā te whakarea x^{4} ki te tau huripoki o \frac{1}{4}.
x^{4}\times 4\times \frac{\frac{1}{2}\times \frac{1}{2}}{x^{3}}
Me whakakore tahi te x^{3} i te taurunga me te tauraro.
x^{4}\times 4\times \frac{\frac{1}{4}}{x^{3}}
Whakareatia te \frac{1}{2} ki te \frac{1}{2}, ka \frac{1}{4}.
x^{4}\times 4\times \frac{1}{4x^{3}}
Tuhia te \frac{\frac{1}{4}}{x^{3}} hei hautanga kotahi.
\frac{x^{4}}{4x^{3}}\times 4
Tuhia te x^{4}\times \frac{1}{4x^{3}} hei hautanga kotahi.
\frac{x}{4}\times 4
Me whakakore tahi te x^{3} i te taurunga me te tauraro.
x
Me whakakore te 4 me te 4.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{4}x^{3}}{x\times \frac{1}{2}xx\times \frac{1}{2}}\times \frac{x\times \frac{1}{2}xx\times \frac{1}{2}}{x^{2}xx^{3}})
Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 3 me te 1 kia riro ai te 4.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{7}}{x\times \frac{1}{2}xx\times \frac{1}{2}}\times \frac{x\times \frac{1}{2}xx\times \frac{1}{2}}{x^{2}xx^{3}})
Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 4 me te 3 kia riro ai te 7.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{7}}{x^{2}\times \frac{1}{2}x\times \frac{1}{2}}\times \frac{x\times \frac{1}{2}xx\times \frac{1}{2}}{x^{2}xx^{3}})
Whakareatia te x ki te x, ka x^{2}.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x\times \frac{1}{2}xx\times \frac{1}{2}}{x^{2}xx^{3}})
Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 2 me te 1 kia riro ai te 3.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x^{2}\times \frac{1}{2}x\times \frac{1}{2}}{x^{2}xx^{3}})
Whakareatia te x ki te x, ka x^{2}.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{2}xx^{3}})
Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 2 me te 1 kia riro ai te 3.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{3}x^{3}})
Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 2 me te 1 kia riro ai te 3.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{7}}{x^{3}\times \frac{1}{2}\times \frac{1}{2}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{6}})
Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 3 me te 3 kia riro ai te 6.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{4}}{\frac{1}{2}\times \frac{1}{2}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{6}})
Me whakakore tahi te x^{3} i te taurunga me te tauraro.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{4}}{\frac{1}{4}}\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{6}})
Whakareatia te \frac{1}{2} ki te \frac{1}{2}, ka \frac{1}{4}.
\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}\times 4\times \frac{x^{3}\times \frac{1}{2}\times \frac{1}{2}}{x^{6}})
Whakawehe x^{4} ki te \frac{1}{4} mā te whakarea x^{4} ki te tau huripoki o \frac{1}{4}.
\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}\times 4\times \frac{\frac{1}{2}\times \frac{1}{2}}{x^{3}})
Me whakakore tahi te x^{3} i te taurunga me te tauraro.
\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}\times 4\times \frac{\frac{1}{4}}{x^{3}})
Whakareatia te \frac{1}{2} ki te \frac{1}{2}, ka \frac{1}{4}.
\frac{\mathrm{d}}{\mathrm{d}x}(x^{4}\times 4\times \frac{1}{4x^{3}})
Tuhia te \frac{\frac{1}{4}}{x^{3}} hei hautanga kotahi.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{4}}{4x^{3}}\times 4)
Tuhia te x^{4}\times \frac{1}{4x^{3}} hei hautanga kotahi.
\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x}{4}\times 4)
Me whakakore tahi te x^{3} i te taurunga me te tauraro.
\frac{\mathrm{d}}{\mathrm{d}x}(x)
Me whakakore te 4 me te 4.
x^{1-1}
Ko te pārōnaki o ax^{n} ko nax^{n-1}.
x^{0}
Tango 1 mai i 1.
1
Mō tētahi kupu t mahue te 0, t^{0}=1.