Løs 13m01*602*10^23

$$13 m 01 \cdot 602 \cdot 10 ^ { 23 }$$

Evaluer

$$782600000000000000000000000m_{0}$$

Løsningsvejledning

Multiplicer 13 og 1 for at få 13.

$$13m_{0}\times 602\times 10^{23}$$

Multiplicer 13 og 602 for at få 7826.

$$7826m_{0}\times 10^{23}$$

Beregn 10 til potensen af 23, og få 100000000000000000000000.

$$7826m_{0}\times 100000000000000000000000$$

Multiplicer 7826 og 100000000000000000000000 for at få 782600000000000000000000000.

$$782600000000000000000000000m_{0}$$

Differentier w.r.t. m_0

$$782600000000000000000000000$$

Vejledning i brug af definition af en afledning

Multiplicer 13 og 1 for at få 13.

$$\frac{\mathrm{d}}{\mathrm{d}m_{0}}(13m_{0}\times 602\times 10^{23})$$

Multiplicer 13 og 602 for at få 7826.

$$\frac{\mathrm{d}}{\mathrm{d}m_{0}}(7826m_{0}\times 10^{23})$$

Beregn 10 til potensen af 23, og få 100000000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}m_{0}}(7826m_{0}\times 100000000000000000000000)$$

Multiplicer 7826 og 100000000000000000000000 for at få 782600000000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}m_{0}}(782600000000000000000000000m_{0})$$

Afledningen af ax^{n} er nax^{n-1}.

$$782600000000000000000000000m_{0}^{1-1}$$

Subtraher 1 fra 1.

$$782600000000000000000000000m_{0}^{0}$$

For ethvert led t bortset fra 0, t^{0}=1.

$$782600000000000000000000000\times 1$$

For ethvert led t, t\times 1=t og 1t=t.

$$782600000000000000000000000$$