Whakaoti i te x/frac{3{9}}+x/25/100+frac{x/2}{10}+frac{frac{x}{15}}{90}

$$\frac{ x }{ \frac{ 3 }{ 9 } } + \frac{ \frac{ x }{ 25 } }{ 100 } + \frac{ \frac{ x }{ 2 } }{ 10 } + \frac{ \frac{ x }{ 15 } }{ 90 }$$

Aromātai

$$\frac{51488x}{16875}$$

Ngā Upane Otinga

Whakawehe x ki te \frac{3}{9} mā te whakarea x ki te tau huripoki o \frac{3}{9}.

$$\frac{x\times 9}{3}+\frac{\frac{x}{25}}{100}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90}$$

Whakawehea te x\times 9 ki te 3, kia riro ko x\times 3.

$$x\times 3+\frac{\frac{x}{25}}{100}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90}$$

Tuhia te \frac{\frac{x}{25}}{100} hei hautanga kotahi.

$$x\times 3+\frac{x}{25\times 100}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90}$$

Whakareatia te 25 ki te 100, ka 2500.

$$x\times 3+\frac{x}{2500}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90}$$

Pahekotia te x\times 3 me \frac{x}{2500}, ka \frac{7501}{2500}x.

$$\frac{7501}{2500}x+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90}$$

Tuhia te \frac{\frac{x}{2}}{10} hei hautanga kotahi.

$$\frac{7501}{2500}x+\frac{x}{2\times 10}+\frac{\frac{x}{15}}{90}$$

Whakareatia te 2 ki te 10, ka 20.

$$\frac{7501}{2500}x+\frac{x}{20}+\frac{\frac{x}{15}}{90}$$

Pahekotia te \frac{7501}{2500}x me \frac{x}{20}, ka \frac{3813}{1250}x.

$$\frac{3813}{1250}x+\frac{\frac{x}{15}}{90}$$

Tuhia te \frac{\frac{x}{15}}{90} hei hautanga kotahi.

$$\frac{3813}{1250}x+\frac{x}{15\times 90}$$

Whakareatia te 15 ki te 90, ka 1350.

$$\frac{3813}{1250}x+\frac{x}{1350}$$

Pahekotia te \frac{3813}{1250}x me \frac{x}{1350}, ka \frac{51488}{16875}x.

$$\frac{51488}{16875}x$$

Kimi Pārōnaki e ai ki x

$$\frac{51488}{16875} = 3\frac{863}{16875} = 3.051140740740741$$

Ngā Upane e Whakamahi ana i te Tautuhinga o te Pārōnaki

Whakawehe x ki te \frac{3}{9} mā te whakarea x ki te tau huripoki o \frac{3}{9}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x\times 9}{3}+\frac{\frac{x}{25}}{100}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90})$$

Whakawehea te x\times 9 ki te 3, kia riro ko x\times 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 3+\frac{\frac{x}{25}}{100}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90})$$

Tuhia te \frac{\frac{x}{25}}{100} hei hautanga kotahi.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 3+\frac{x}{25\times 100}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90})$$

Whakareatia te 25 ki te 100, ka 2500.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times 3+\frac{x}{2500}+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90})$$

Pahekotia te x\times 3 me \frac{x}{2500}, ka \frac{7501}{2500}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7501}{2500}x+\frac{\frac{x}{2}}{10}+\frac{\frac{x}{15}}{90})$$

Tuhia te \frac{\frac{x}{2}}{10} hei hautanga kotahi.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7501}{2500}x+\frac{x}{2\times 10}+\frac{\frac{x}{15}}{90})$$

Whakareatia te 2 ki te 10, ka 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{7501}{2500}x+\frac{x}{20}+\frac{\frac{x}{15}}{90})$$

Pahekotia te \frac{7501}{2500}x me \frac{x}{20}, ka \frac{3813}{1250}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3813}{1250}x+\frac{\frac{x}{15}}{90})$$

Tuhia te \frac{\frac{x}{15}}{90} hei hautanga kotahi.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3813}{1250}x+\frac{x}{15\times 90})$$

Whakareatia te 15 ki te 90, ka 1350.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3813}{1250}x+\frac{x}{1350})$$

Pahekotia te \frac{3813}{1250}x me \frac{x}{1350}, ka \frac{51488}{16875}x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{51488}{16875}x)$$

Ko te pārōnaki o ax^{n} ko nax^{n-1}.

$$\frac{51488}{16875}x^{1-1}$$

Tango 1 mai i 1.

$$\frac{51488}{16875}x^{0}$$

Mō tētahi kupu t mahue te 0, t^{0}=1.

$$\frac{51488}{16875}\times 1$$

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

$$\frac{51488}{16875}$$