Answer
(a) -2
(b) $-\frac{3}{8}$
(c) 6
Work Step by Step
$f(x)$ is the value of the function at the point $x$
$f'(x)$ is the slope of the graph at the point $x$
(a) $P(x) = f(x)g(x)$
$P'(x) = f'(x)g(x)+f(x)g'(x)$
$P'(2) = f'(2)g(2)+f(2)g'(2)$
$P'(2) = (-1)(4)+(1)(2)$
$P'(2) = -2$
(b) $Q(x) = \frac{f(x)}{g(x)}$
$Q'(x) = \frac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}$
$Q'(2) = \frac{f'(2)g(2)-f(2)g'(2)}{[g(2)]^2}$
$Q'(2) = \frac{(-1)(4)-(1)(2)}{(4)^2}$
$Q'(2) = -\frac{3}{8}$
(c) $C(x) = f(g(x))$
$C'(x) = f'(g(x))~g'(x)$
$C'(2) = f'(g(2))~g'(2)$
$C'(2) = f'(4)~g'(2)$
$C'(2) = (3)(2)$
$C'(2) = 6$
