Whakaoti i te 10^-63^-7625*x^-4div5^-3*{6}^-5*{x}^-8

$${ 10 }^{ -6 } { 3 }^{ -7 } 625 \times { x }^{ -4 } \div { 5 }^{ -3 } \times { 6 }^{ -5 } \times { x }^{ -8 }$$

Aromātai

$$\frac{5}{1088391168x^{12}}$$

Ngā Upane Otinga

Tātaihia te 10 mā te pū o -6, kia riro ko \frac{1}{1000000}.

$$\frac{\frac{1}{1000000}\times 3^{-7}\times 625x^{-4}}{5^{-3}}\times 6^{-5}x^{-8}$$

Tātaihia te 3 mā te pū o -7, kia riro ko \frac{1}{2187}.

$$\frac{\frac{1}{1000000}\times \frac{1}{2187}\times 625x^{-4}}{5^{-3}}\times 6^{-5}x^{-8}$$

Whakareatia te \frac{1}{1000000} ki te \frac{1}{2187}, ka \frac{1}{2187000000}.

$$\frac{\frac{1}{2187000000}\times 625x^{-4}}{5^{-3}}\times 6^{-5}x^{-8}$$

Whakareatia te \frac{1}{2187000000} ki te 625, ka \frac{1}{3499200}.

$$\frac{\frac{1}{3499200}x^{-4}}{5^{-3}}\times 6^{-5}x^{-8}$$

Tātaihia te 5 mā te pū o -3, kia riro ko \frac{1}{125}.

$$\frac{\frac{1}{3499200}x^{-4}}{\frac{1}{125}}\times 6^{-5}x^{-8}$$

Whakawehe \frac{1}{3499200}x^{-4} ki te \frac{1}{125} mā te whakarea \frac{1}{3499200}x^{-4} ki te tau huripoki o \frac{1}{125}.

$$\frac{1}{3499200}x^{-4}\times 125\times 6^{-5}x^{-8}$$

Whakareatia te \frac{1}{3499200} ki te 125, ka \frac{5}{139968}.

$$\frac{5}{139968}x^{-4}\times 6^{-5}x^{-8}$$

Tātaihia te 6 mā te pū o -5, kia riro ko \frac{1}{7776}.

$$\frac{5}{139968}x^{-4}\times \frac{1}{7776}x^{-8}$$

Whakareatia te \frac{5}{139968} ki te \frac{1}{7776}, ka \frac{5}{1088391168}.

$$\frac{5}{1088391168}x^{-4}x^{-8}$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te -4 me te -8 kia riro ai te -12.

$$\frac{5}{1088391168}x^{-12}$$

Kimi Pārōnaki e ai ki x

$$-\frac{5}{90699264x^{13}}$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Pārōnaki

Tātaihia te 10 mā te pū o -6, kia riro ko \frac{1}{1000000}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{1000000}\times 3^{-7}\times 625x^{-4}}{5^{-3}}\times 6^{-5}x^{-8})$$

Tātaihia te 3 mā te pū o -7, kia riro ko \frac{1}{2187}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{1000000}\times \frac{1}{2187}\times 625x^{-4}}{5^{-3}}\times 6^{-5}x^{-8})$$

Whakareatia te \frac{1}{1000000} ki te \frac{1}{2187}, ka \frac{1}{2187000000}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{2187000000}\times 625x^{-4}}{5^{-3}}\times 6^{-5}x^{-8})$$

Whakareatia te \frac{1}{2187000000} ki te 625, ka \frac{1}{3499200}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{3499200}x^{-4}}{5^{-3}}\times 6^{-5}x^{-8})$$

Tātaihia te 5 mā te pū o -3, kia riro ko \frac{1}{125}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{1}{3499200}x^{-4}}{\frac{1}{125}}\times 6^{-5}x^{-8})$$

Whakawehe \frac{1}{3499200}x^{-4} ki te \frac{1}{125} mā te whakarea \frac{1}{3499200}x^{-4} ki te tau huripoki o \frac{1}{125}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{3499200}x^{-4}\times 125\times 6^{-5}x^{-8})$$

Whakareatia te \frac{1}{3499200} ki te 125, ka \frac{5}{139968}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{139968}x^{-4}\times 6^{-5}x^{-8})$$

Tātaihia te 6 mā te pū o -5, kia riro ko \frac{1}{7776}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{139968}x^{-4}\times \frac{1}{7776}x^{-8})$$

Whakareatia te \frac{5}{139968} ki te \frac{1}{7776}, ka \frac{5}{1088391168}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{1088391168}x^{-4}x^{-8})$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te -4 me te -8 kia riro ai te -12.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{5}{1088391168}x^{-12})$$

Ko te pārōnaki o ax^{n} ko nax^{n-1}.

$$-12\times \frac{5}{1088391168}x^{-12-1}$$

Whakareatia -12 ki te \frac{5}{1088391168}.

$$-\frac{5}{90699264}x^{-12-1}$$

Tango 1 mai i -12.

$$-\frac{5}{90699264}x^{-13}$$