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Index  Inference Rule  Input latex  Feeds latex  Output latex  step validity  dimension check  unit check  notes 

5  substitute LHS of expr 1 into expr 2 



LHS diff is nabla**2*(pdg2718(pdg1467*pdg2321*pdg4621)  exp(pdg1467*pdg2321*pdg4621))*pdg6238(pdg9472) RHS diff is partial*pdg6197*pdg7940*(pdg2718(pdg1467*pdg2321*pdg4621)  exp(pdg1467*pdg2321*pdg4621))*pdg6238(pdg9472)/pdg1467**2 
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9394939493: 2029293929: 
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6  differentiate with respect to 



no check performed 
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2  declare initial expr 



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3  declare guess solution 



no validation is available for declarations 
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4  substitute LHS of expr 1 into expr 2 



valid 
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8494839423: 9394939493: 
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7  differentiate with respect to 



no check performed 
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1858578388: 

10  simplify 



LHS diff is nabla**2*(pdg2718(pdg1467*pdg2321*pdg4621)  1)*pdg6238(pdg9472) RHS diff is pdg2321**2*(1  pdg2718(pdg1467*pdg2321*pdg4621))*pdg6238(pdg9472)/pdg4567**2 
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11  declare final expr 



no validation is available for declarations 
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9  substitute LHS of expr 1 into expr 2 



LHS diff is nabla**2*pdg2718(pdg1467*pdg2321*pdg4621)*pdg6238(pdg9472) + pdg6197*pdg7940 RHS diff is (pdg2321**2*pdg2718(pdg1467*pdg2321*pdg4621)*pdg6238(pdg9472) + 1)/pdg4567**2 
1858578388:
4585828572: dimensions are consistent 9485384858: 
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4585828572: N/A 9485384858: 

1  declare initial expr 



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8  declare initial expr 



no validation is available for declarations 
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dimensions are consistent 
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N/A 
symbol ID  category  latex  scope  dimension  name  value  Used in derivations  references  

2718  constant 
\exp
\(\exp\) 
['real'] 

e 
2.71828 unitless 
8  
4567  constant 
c
\(c\) 
['real'] 

speed of light in vacuum 
299792458 meters/second 
32  
9472  variable 
\vec{r}
\(\vec{r}\) 
real 

radius vector 

24  
6197  constant 
\mu_0
\(\mu_0\) 
real 

vacuum permeability, permeability of free space, permeability of vacuum, or magnetic constant 
1.25663706212E^{6} N/A^2 
8  
6238  variable 
E
\(E\) 
real  dimensionless  electric field  20  
1467  variable 
t
\(t\) 
['real'] 

time 

120  
7940  constant 
\epsilon_0
\(\epsilon_0\) 
real 

vacuum permittivity, permittivity of free space or electric constant or the distributed capacitance of the vacuum 
8.8541878128E{12} F/m 
14  
2321  variable 
\omega
\(\omega\) 
['real'] 

angular frequency  21  
4621  variable 
i
\(i\) 
['imaginary'] 

imaginary unit 

74  
4326  variable 
\vec{E}
\(\vec{E}\) 
complex  dimensionless  electric field  9 