This page contains three views of the steps in the derivation: d3js, graphviz PNG, and a table.
Notes for this derivation:
Index | Inference Rule | Input latex | Feeds latex | Output latex | step validity | dimension check | unit check | notes |
---|---|---|---|---|---|---|---|---|
14 | replace scalar with vector |
|
|
|
no check performed |
9999999870:
9999998870: |
9999999870:
9999998870: |
|
17 | substitute RHS of expr 1 into expr 2 |
|
|
|
LHS diff is -pdg9489(pdg9472, pdg1467) + pdg4931/pdg1054 RHS diff is pdg2321 - pdg8330*pdg2718(pdg4621((pdg1134*pdg9472 - pdg1467*pdg6238)/pdg1054)) |
3948574226:
9999999961: 3948574228: |
3948574226:
9999999961: 3948574228: |
|
1 | declare initial expr |
|
|
|
no validation is available for declarations |
3121513111:
|
3121513111:
|
|
19 | declare initial expr |
|
|
|
no validation is available for declarations |
1029039903:
|
1029039903:
|
|
11 | substitute RHS of expr 1 into expr 2 |
|
|
|
LHS diff is -pdg1134 + pdg5321/(2*pdg3141) RHS diff is pdg1115 - pdg4413*pdg5321/(2*pdg3141) |
1020394900:
dimensions are consistent 3121234211: 3121234212: |
1020394900:
N/A 3121234211: 3121234212: |
|
3 | declare initial expr |
|
|
|
no validation is available for declarations |
9999999960:
|
9999999960:
|
|
7 | substitute RHS of expr 1 into expr 2 |
|
|
|
valid |
3147472131:
1020394902: 4147472132: |
3147472131:
1020394902: 4147472132: |
|
18 | simplify |
|
|
|
LHS diff is 0 RHS diff is pdg8330*(-pdg2718(pdg4621*(pdg1134*pdg9472 - pdg1467*pdg6238)/pdg1054) + pdg2718(pdg4621((pdg1134*pdg9472 - pdg1467*pdg6238)/pdg1054))) |
3948574228:
3948574230: |
3948574228:
3948574230: |
|
24 | partially differentiate with respect to |
|
|
|
no check performed |
3948574230:
3948574233: |
3948574230:
3948574233: |
|
20 | declare initial expr |
|
|
|
no validation is available for declarations |
4298359835:
|
4298359835:
|
|
15 | declare initial expr |
|
|
|
no validation is available for declarations |
3948574224:
|
3948574224:
|
|
13 | divide both sides by |
|
|
|
valid |
9999999962:
9999999870: |
9999999962:
9999999870: |
|
22 | multiply RHS by unity |
|
|
|
valid |
4298359835:
4298359845: |
4298359835:
4298359845: |
|
32 | simplify |
|
|
|
failed |
4394958389:
1648958381: |
4394958389:
1648958381: |
|
21 | raise both sides to power |
|
|
|
no check is performed |
1029039903:
1029039904: |
1029039903:
1029039904: |
|
23 | substitute RHS of expr 1 into expr 2 |
|
|
|
LHS diff is 0 RHS diff is (-pdg1134**2 + pdg1357**2*pdg5156**2)/(2*pdg5156) |
1029039904:
4298359845: 4298359851: |
1029039904:
4298359845: 4298359851: |
|
28 | apply gradient to scalar function |
|
|
|
no check performed |
3948574230:
3948574230: |
3948574230:
3948574230: |
|
37 | declare initial expr |
|
|
|
no validation is available for declarations |
1158485859:
|
1158485859:
|
|
25 | substitute RHS of expr 1 into expr 2 |
|
|
|
LHS diff is pdg9489(pdg9472, pdg1467) - Derivative(pdg9489(pdg9472, pdg1467), pdg1467) RHS diff is (pdg1054*pdg8330*pdg2718(pdg4621*(pdg1134*pdg9472 - pdg1467*pdg6238)/pdg1054) + pdg4621*pdg6238*pdg9489(pdg9472, pdg1467))/pdg1054 |
3948574233:
3948574230: 3948571256: |
3948574233:
3948574230: 3948571256: |
|
10 | divide both sides by |
|
|
|
LHS diff is 0 RHS diff is -pdg1115 + 1/pdg1115 |
3121513111:
3121234211: |
3121513111:
3121234211: |
|
2 | declare initial expr |
|
|
|
no validation is available for declarations |
3131211131:
|
3131211131:
|
|
8 | substitute RHS of expr 1 into expr 2 |
|
|
|
valid |
9999999960:
4147472132: 9999999965: |
9999999960:
4147472132: 9999999965: |
|
16 | substitute RHS of expr 1 into expr 2 |
|
|
|
LHS diff is -pdg9489(pdg9472, pdg1467) + pdg2046/pdg1054 RHS diff is pdg7394 - pdg8330*pdg2718(pdg4621(-pdg1467*pdg2321 + pdg1134*pdg9472/pdg1054)) |
3948574224:
9999998870: 3948574226: |
3948574224:
9999998870: 3948574226: |
|
12 | substitute RHS of expr 1 into expr 2 |
|
|
|
LHS diff is pdg1054 - pdg1134 RHS diff is -pdg1054*pdg5321 + pdg4413/(2*pdg3141) |
3121234212:
9999999960: 9999999962: |
3121234212:
9999999960: 9999999962: |
|
38 | substitute LHS of expr 1 into expr 2 |
|
|
|
Nothing to split |
1158485859:
9958485859: 2258485859: |
1158485859:
9958485859: 2258485859: |
|
31 | apply divergence |
|
|
|
failed |
5985371230:
4394958389: |
5985371230:
4394958389: |
|
26 | substitute RHS of expr 1 into expr 2 |
|
|
|
LHS diff is 0 RHS diff is pdg4621*(pdg1134**2 - 2*pdg5156*pdg6238)*pdg9489(pdg9472, pdg1467)/(2*pdg1054*pdg5156) |
4298359851:
3948571256: 4348571256: |
4298359851:
3948571256: 4348571256: |
|
9 | divide both sides by |
|
|
|
valid |
9999999965:
9999999961: |
9999999965:
9999999961: |
|
5 | declare initial expr |
|
|
|
no validation is available for declarations |
1020394902:
|
1020394902:
|
|
6 | divide both sides by |
|
|
|
valid |
3131211131:
3147472131: |
3131211131:
3147472131: |
|
33 | substitute RHS of expr 1 into expr 2 |
|
|
|
Nothing to split |
5985371230:
1648958381: 2648958382: |
5985371230:
1648958381: 2648958382: |
|
34 | simplify |
|
|
|
Nothing to split |
2648958382:
2395958385: |
2648958382:
2395958385: |
|
27 | multiply both sides by |
|
|
|
LHS diff is 0 RHS diff is pdg1134**2*(-pdg4621**2 - 1)*pdg9489(pdg9472, pdg1467)/(2*pdg5156) |
4348571256:
4341171256: |
4348571256:
4341171256: |
|
35 | multiply both sides by |
|
|
|
LHS diff is 0 RHS diff is pdg1134**2*(pdg1054 - 1)*pdg9489(pdg9472, pdg1467)/(2*pdg5156) |
2395958385:
5868688585: |
2395958385:
5868688585: |
|
30 | substitute RHS of expr 1 into expr 2 |
|
|
|
failed |
4943571230:
3948574230: 5985371230: |
4943571230:
3948574230: 5985371230: |
|
29 | simplify |
|
|
|
failed |
3948574230:
4943571230: |
3948574230:
4943571230: |
|
39 | declare final expr |
|
|
|
no validation is available for declarations |
2258485859:
|
2258485859:
|
|
36 | LHS of expr 1 equals LHS of expr 2 |
|
|
|
Nothing to split |
4341171256:
5868688585: 9958485859: |
4341171256:
5868688585: 9958485859: |
|
4 | declare initial expr |
|
|
|
no validation is available for declarations |
1020394900:
dimensions are consistent |
1020394900:
N/A |