About the properties of the Divergence of a vector field

[aboutammam]

Hello
I have a question if it possible,
Let X a tangantial vector field of a riemannian manifolds M, and f a smooth function define on M.
Is it true that X(exp-f)=-exp(-f).X(f)
And div( exp(-f).X)=exp(-f)〈gradf, X〉+exp(-f)div(X)?
Thank you

 

[Orodruin]

These should be fairly simple things to derive yourself.