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How to differentiate partial derivatives?
I have the equation y''= 2y - xy' and i need to differentiate to obtain the third derivative but im not sure as to what the xy' term becomes when differentiated
2 Answers
- Dragon.JadeLv 75 years agoFavorite Answer
Hello,
NOTE: if my question is illegible, use a browser that displays Unicode characters like Firefox or Edge...
= = = = = = = = = = = = = = = =
βΊ Remember product law:
Β Β (πΒ·π)' = π'Β·π + πΒ·π'
So when π=π₯ and π=π¦' :
Β Β (π₯Β·π¦') = 1Β·π¦' + π₯Β·π¦" = π¦' + π₯Β·π¦"
βΊ Which means:
Β Β π¦" = 2π¦ β π₯Β·π¦'
yields by derivation:
Β Β π¦"' = 2π¦' β (π¦' + π₯Β·π¦") = 2π¦' β π¦' β π₯Β·π¦" = π¦' β π₯Β·π¦"
Regards,
Dragon.Jade :-)
- cidyahLv 75 years ago
y'' = 2y - xy'
y''' = 2y' - x y''
If it is partial derivative, xy' becomes x y'' when differentiated. else, it becomes y' + x y''
