Rešite x/frac{3{9}}+x/25/100+frac{x/2}{10}+frac{frac{x}{15}}{90}

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

Ovrednoti

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

Koraki rešitve

Delite x s/z \frac{3}{9} tako, da pomnožite x z obratno vrednostjo \frac{3}{9}.

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

Delite x\times 9 s/z 3, da dobite x\times 3.

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

Izrazite \frac{\frac{x}{25}}{100} kot enojni ulomek.

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

Pomnožite 25 in 100, da dobite 2500.

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

Združite x\times 3 in \frac{x}{2500}, da dobite \frac{7501}{2500}x.

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

Izrazite \frac{\frac{x}{2}}{10} kot enojni ulomek.

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

Pomnožite 2 in 10, da dobite 20.

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

Združite \frac{7501}{2500}x in \frac{x}{20}, da dobite \frac{3813}{1250}x.

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

Izrazite \frac{\frac{x}{15}}{90} kot enojni ulomek.

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

Pomnožite 15 in 90, da dobite 1350.

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

Združite \frac{3813}{1250}x in \frac{x}{1350}, da dobite \frac{51488}{16875}x.

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

Odvajajte w.r.t. x

$$\frac{51488}{16875} = 3\frac{863}{16875} = 3,051140740740741$$

Koraki z uporabo definicije odvoda

Delite x s/z \frac{3}{9} tako, da pomnožite x z obratno vrednostjo \frac{3}{9}.

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

Delite x\times 9 s/z 3, da dobite x\times 3.

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

Izrazite \frac{\frac{x}{25}}{100} kot enojni ulomek.

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

Pomnožite 25 in 100, da dobite 2500.

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

Združite x\times 3 in \frac{x}{2500}, da dobite \frac{7501}{2500}x.

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

Izrazite \frac{\frac{x}{2}}{10} kot enojni ulomek.

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

Pomnožite 2 in 10, da dobite 20.

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

Združite \frac{7501}{2500}x in \frac{x}{20}, da dobite \frac{3813}{1250}x.

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

Izrazite \frac{\frac{x}{15}}{90} kot enojni ulomek.

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

Pomnožite 15 in 90, da dobite 1350.

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

Združite \frac{3813}{1250}x in \frac{x}{1350}, da dobite \frac{51488}{16875}x.

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

Odvod ax^{n} je nax^{n-1}.

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

Odštejte 1 od 1.

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

Za kakršen koli izraz t, razen 0, t^{0}=1.

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

Za kakršen koli izraz t, t\times 1=t in 1t=t.

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