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eg. Find the directional derivative of the function phi=xyz^2 at the point (1,2,3).
Actually what is the math used for?
Let's say
phi is the temperature of air(scalar field).
∇phi will be the rate if change of temperature at (1,2,3), why the direction come out.
directional derivative of it is the velocity of air(vector field)?
If so , can I say directional derivative of it is the direction of the air?
actually this is the conclusion I made from my own study.
please give me a simple example.
Thank you
Actually what is the math used for?
Let's say
phi is the temperature of air(scalar field).
∇phi will be the rate if change of temperature at (1,2,3), why the direction come out.
directional derivative of it is the velocity of air(vector field)?
If so , can I say directional derivative of it is the direction of the air?
actually this is the conclusion I made from my own study.
please give me a simple example.
Thank you