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  • Oct 15, 2018, 07:02 AM
    aboutammam
    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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