Gradient of function in terms of retarded time produces time derivative

In Griffith’s introduction to electromagnetism on page 479, there is this following equation:

begin{align*}
nabla V &cong nabla left[frac{1}{4pi epsilon_0} frac{boldsymbol{hat r} cdot dot{mathbf{p}}(t_0)}{rc} right]
&cong left[frac{1}{4pi epsilon_0} frac{boldsymbol{hat r} cdot ddot{mathbf{p}}(t_0)}{rc} right] nabla t_0
&= -frac{1}{4pi epsilon_0 c^2} frac{[boldsymbol{hat r} cdot ddot{mathbf{p}}(t_0)]}{r} boldsymbol{hat{r}}
end{align*}

given that $t_0equiv t – dfrac{r}{c}$. Why is it that one the second line the dipole moment — the $p$ function — gains an extra time derivative if the gradient is in terms of partial spatial derivatives?