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October 15th, 2018, 06:49 AM  #1 
Newbie Joined: Oct 2015 From: algeria Posts: 4 Thanks: 0  Directional derivative of exponential of a function
I have a trouble of a directional derivative of a function : for a function f and a tangent vector field X of a manifold M, we have X(f)=âˆ‡_{X}f=<âˆ‡f,X> From this above formula, is it true that : X(e^{f})=<âˆ‡e^{f},X>=<e^{f}âˆ‡(f),X>=e^{f}<âˆ‡f,X> If it not true, what is X(e^{f})? 

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derivative, directional, exponential, function 
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