 Ask Remember Me? aboutammam Posts: 1, Reputation: 1 New Member #1 Oct 15, 2018, 07:02 AM
Directional derivative of exponential of a function
Hello
I have a question if it possible
for a function f and a tangent vector field X of a manifold M, we have

X(f)=∇_{X}f=<∇f,X>

From this above formula, is it true that :

X(e^{-f})=<∇e^{-f},X>=<e^{-f}∇(-f),X>=-e^{-f}<∇f,X>

If it not true, what is X(e^{-f})?

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