Derive the following strings with the grammar of Figure $7\mathrm{.}2$ and draw the corresponding syntax tree: $*($a$)-$d $($b$)+$ddd $($c$)$ d FIGURE $7\mathrm{.}2$ A grammar for signed integers.

N$=\{$I$,$ F$,$ M$\}$

T$=\{+,-,$ d$\}$

P$=$ the productions

$1.$ I$->$FM

$2.$ F$->+$

$3.$ F$->-$

$4.$ F$->\backslash$epsi

$5.$ M$->$dM

$6.$ M$->$d

S$=$ I