Is this function convex ? (Riemannian geometry)

Let $f:Mtomathbb R$ be a geodesically convex function on a Riemannian manifold $M$, assumed to have nonpositive sectional curvature.

Fix $x_0in M$ and let $g:T_{x_0}Mtomathbb R$ the map defined by $g(u)=f(exp_{x_0}(u))$.

Is $g$ convex ?