$(20$ points$)$ Consider the following grammars $G_1$ and $G_2$ :

$G_1$:

$S$xAx

$AAa|Ab|c|d$

$G_2$:

$S$xAx

$Ac|d|cB|dB$

$BaB|bB|a|b$

$($a$)$ Give a derivation sequence for string xcabx in $G_1.$ Give the derivation tree of the sequence.

$($b$)$ Give a derivation sequence for string xcabx in $G_2.$ Give the derivation tree of the sequence.