Derivative of the fundamental solution of the heat equation Let $\Gamma$ be the fundamental solution of the heat equation in $(0,\infty)\times\mathbb{R}^n$, that is 
\begin{equation}
\Gamma(t,x)=\frac{1}{(4\pi t)^{\frac{n}{2}}}e^{\frac{-|x|^2}{4t}} \mbox{ per }x\in\mathbb{R}^n,t>0.
\end{equation} 
In the book by Ladyzhenskaya,Solonnikov and Ural'tseva "Linear and Quasi-linear Equations of Parabolic Type" at page 274 is stated this inequality
\begin{equation}
|D_t^rD_x^s\Gamma(t,x)|\leq C_{r,s}t^{-\frac{n}{2}-r-\frac{s}{2}}e^{C\frac{-|x|^2}{t}}.
\end{equation}
It's correct?
The exponent of $t$ in the inequality won't be $-\frac{n}{2}-2r-s$ or I have made an  error in the computations?

Yes, it is correct. Say, each differentiation w.r.t. $t$ adds $-1$ to the exponent of $t$.
