Let $(M,g)$ a riemannian manifold. Let $r$ de radial distance i.e
$r(q) = |\exp_p^{-1}(q)|$
define
$\frac{\partial}{\partial r} = \sum_i \frac{x_i}{r}\frac{\partial}{\partial x_i}$
in this book said that
$\frac{\partial}{\partial r} = \frac{d}{dt}_{t = 0}\exp_p(t\frac{v}{|v|}+v)$
where $v \in T_pM$ with $\exp_p(v) = q$.
but why this is true??