We denote $\mathcal { D }$ the open unit disk of $\mathbb { C } : \mathcal { D } = \{ z \in \mathbb { C } ; | z | < 1 \}$. We define the function $\varphi : \mathbb { R } \rightarrow \mathbb { R }$ by
$$\begin{cases} \varphi ( x ) = \exp \left( \frac { - x } { \sqrt { 1 - x } } \right) & \text { if } x < 1 \\ \varphi ( x ) = 0 & \text { if } x \geqslant 1 \end{cases}$$
Justify that, for all $p \in \mathbb { N }$, the function $\varphi ^ { ( p ) }$ is bounded on $] - 1,1 [$.