Løs G6674*10^-1170^273510^22/173^2

$$G6674 \times { 10 }^{ -11 } \frac{ { 70 }^{ 2 } 735 { 10 }^{ 22 } }{ { 173 }^{ 2 } }$$

Evaluer

$$\frac{360150000000000000G_{6674}}{29929}$$

Løsningsvejledning

Beregn 10 til potensen af -11, og få \frac{1}{100000000000}.

$$G_{6674}\times \frac{1}{100000000000}\times \frac{70^{2}\times 735\times 10^{22}}{173^{2}}$$

Beregn 70 til potensen af 2, og få 4900.

$$G_{6674}\times \frac{1}{100000000000}\times \frac{4900\times 735\times 10^{22}}{173^{2}}$$

Multiplicer 4900 og 735 for at få 3601500.

$$G_{6674}\times \frac{1}{100000000000}\times \frac{3601500\times 10^{22}}{173^{2}}$$

Beregn 10 til potensen af 22, og få 10000000000000000000000.

$$G_{6674}\times \frac{1}{100000000000}\times \frac{3601500\times 10000000000000000000000}{173^{2}}$$

Multiplicer 3601500 og 10000000000000000000000 for at få 36015000000000000000000000000.

$$G_{6674}\times \frac{1}{100000000000}\times \frac{36015000000000000000000000000}{173^{2}}$$

Beregn 173 til potensen af 2, og få 29929.

$$G_{6674}\times \frac{1}{100000000000}\times \frac{36015000000000000000000000000}{29929}$$

Multiplicer \frac{1}{100000000000} og \frac{36015000000000000000000000000}{29929} for at få \frac{360150000000000000}{29929}.

$$G_{6674}\times \frac{360150000000000000}{29929}$$

Differentier w.r.t. G_6674

$$\frac{360150000000000000}{29929} = 12033479234187\frac{17277}{29929} = 12033479234187,578$$

Vejledning i brug af definition af en afledning

Beregn 10 til potensen af -11, og få \frac{1}{100000000000}.

$$\frac{\mathrm{d}}{\mathrm{d}G_{6674}}(G_{6674}\times \frac{1}{100000000000}\times \frac{70^{2}\times 735\times 10^{22}}{173^{2}})$$

Beregn 70 til potensen af 2, og få 4900.

$$\frac{\mathrm{d}}{\mathrm{d}G_{6674}}(G_{6674}\times \frac{1}{100000000000}\times \frac{4900\times 735\times 10^{22}}{173^{2}})$$

Multiplicer 4900 og 735 for at få 3601500.

$$\frac{\mathrm{d}}{\mathrm{d}G_{6674}}(G_{6674}\times \frac{1}{100000000000}\times \frac{3601500\times 10^{22}}{173^{2}})$$

Beregn 10 til potensen af 22, og få 10000000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}G_{6674}}(G_{6674}\times \frac{1}{100000000000}\times \frac{3601500\times 10000000000000000000000}{173^{2}})$$

Multiplicer 3601500 og 10000000000000000000000 for at få 36015000000000000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}G_{6674}}(G_{6674}\times \frac{1}{100000000000}\times \frac{36015000000000000000000000000}{173^{2}})$$

Beregn 173 til potensen af 2, og få 29929.

$$\frac{\mathrm{d}}{\mathrm{d}G_{6674}}(G_{6674}\times \frac{1}{100000000000}\times \frac{36015000000000000000000000000}{29929})$$

Multiplicer \frac{1}{100000000000} og \frac{36015000000000000000000000000}{29929} for at få \frac{360150000000000000}{29929}.

$$\frac{\mathrm{d}}{\mathrm{d}G_{6674}}(G_{6674}\times \frac{360150000000000000}{29929})$$

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

$$\frac{360150000000000000}{29929}G_{6674}^{1-1}$$

Subtraher 1 fra 1.

$$\frac{360150000000000000}{29929}G_{6674}^{0}$$

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

$$\frac{360150000000000000}{29929}\times 1$$

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

$$\frac{360150000000000000}{29929}$$