Reparameterized geodesics - proof

Question

I was reading the proof for the lemma that states that a certain curve c is a reparameterized geodesic if and only if it satisfies $\frac{D\dot{c}}{dt}=f(t)\dot{c}$. The starting point was defining curve c as $c(t):=\gamma (s(t))$ and so $\dot{c}(t)=\dot{\gamma}(s(t))\frac{ds}{dt}(t)$. At certain point we get: $$\nabla_{\dot{c}}\dot{c}=\nabla_{\dot{c}}(\frac{ds}{dt}\dot{\gamma})=(\frac{d^2s}{dt^2})\dot{\gamma}+(\frac{ds}{dt})\nabla_{\dot{\gamma}\frac{ds}{dt}}\dot{\gamma}$$ I understand this comes from applying the properties of the affine connection but I don't get how the term $(\frac{d^2s}{dt^2})\dot{\gamma}$ shows up.