Answer
$a.\quad-2$
$b.\quad-\displaystyle \frac{24}{7}$
Work Step by Step
$D_{x}(f[g(x)]) =f^{\prime}[g(x)]\cdot g^{\prime}(x)$
(a)
$D_{x}(f[g(x)])\quad $ at $x=1$
$=f^{\prime}[g(1)]\cdot g^{\prime}(1)$
... read the table: $g(1)=2,\displaystyle \quad g^{\prime}(1)=\frac{2}{7}$
$=f^{\prime}(2)\displaystyle \cdot(\frac{2}{7})$
... read the table: $f^{\prime}(2)=-7$
$=-7(\displaystyle \frac{2}{7}]$
$=\color{red}{-2}$
(b)
$D_{x}(f[g(x)])\quad$ at $x=2$
$=f^{\prime}[g(2)]\cdot g^{\prime}(2)$
... read the table: $g(2)=3,\displaystyle \quad g^{\prime}(2)=\frac{3}{7}$
$=f^{\prime}(3)\displaystyle \cdot(\frac{3}{7})$
... read the table: $f^{\prime}(3)=-8$
$=-8(\displaystyle \frac{3}{7}]$
$=\displaystyle \color{red}{-\frac{24}{7}}$
