I have a Riemannian manifold $M$ and $p\in M$.
Let $X,Y\in T_p M$ and consider the loops $\gamma _t$ which is the loop obtained from applying $\exp _p$ to the parallelogram spanned by $\sqrt t X,\sqrt t Y$. Denote $Hol _{\gamma_t} :T_p M \to T_p M$ the parallel transport around $\gamma_t$.
Prove that $$\frac{d}{dt} Hol_{\gamma_t} = R(X,Y)$$
I couldn't figure out where to start.
I know that if $P^t_{s_0,s}$ is the parallel transport around $\gamma_t$ from time $s_0$ to time $s$ then for $V\in T_{\gamma_t(s)}M$ we have $$\frac{D}{ds}=\frac{d}{ds}{P^t_{s_0,s}}^{-1}(V(s)) $$ Where the derivative is taken at time $s_0$.
I also know that for a parametrized surface $f:A\subseteq\mathbb{R}^2\to M$ and $V$ some vector field on it with coordinates $s,t$ we have $$\frac{D}{dt}\frac{D}{ds}V-\frac{D}{ds}\frac{D}{dt}V=R(\frac{d}{ds}f,\frac{d}{dt}f)$$
But the image of the parallelogram is not exactly a parametrized surface, to my understanding. Any hint will be helpful, I've been thinking about this question for a few days know.
Someone gave me a hint - to look at $f(s,t)$ the parallel transport of some $Z\in T_pM$ around the parallelogram of sides $sX,tY$. But I don't understand how this helps.