Answer
$a.\quad-\displaystyle \frac{18}{7}$
$b.\quad-5$
Work Step by Step
$D_{x}(f[g(x)]) =f^{\prime}[g(x)]\cdot g^{\prime}(x)$
(a)
$D_{x}(g[f(x)])$ at $x=1$
$=g^{\prime}[f(1)]\cdot f^{\prime}(1)$
... read the table: $f(1)=2,\quad f^{\prime}(1)=-6$
$=g^{\prime}(2)\cdot(-6)$
... read the table:$ g^{\prime}(2)=\displaystyle \frac{3}{7}$
$=\displaystyle \frac{3}{7}(-6)$
$=\displaystyle \color{red}{-\frac{18}{7}}$
(b)
$D_{x}(g[f(x)])$ at $x=2$
$=g^{\prime}[f(2)]\cdot f^{\prime}(2)$
... read the table: $f(2)=4,\quad f^{\prime}(2)=-7$
$=g^{\prime}(4)\cdot(-7)$
... read the table: $g^{\prime}(4)\displaystyle \cdot\frac{5}{7}$
$=\displaystyle \frac{5}{7}(-7)$
$=\color{red}{-5}$
