Answer
(a) 4
(b) 6
(c) $\frac{7}{9}$
(d) 12
Work Step by Step
(a) $S(x) = f(x) + g(x)$
$S'(x) = f'(x)+g'(x)$
$S'(1) = f'(1)+g'(1)$
$S'(1) = 3+1$
$S'(1) = 4$
(b) $P(x) = f(x)g(x)$
$P'(x) = f'(x)g(x)+f(x)g'(x)$
$P'(2) = f'(2)g(2)+f(2)g'(2)$
$P'(2) = (2)(1)+(1)(4)$
$P'(2) = 6$
(c) $Q(x) = \frac{f(x)}{g(x)}$
$Q'(x) = \frac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^2}$
$Q'(1) = \frac{f'(1)g(1)-f(1)g'(1)}{[g(1)]^2}$
$Q'(1) = \frac{(3)(3)-(2)(1)}{(3)^2}$
$Q'(1) = \frac{7}{9}$
(d) $C(x) = f(g(x))$
$C'(x) = f'(g(x))~g'(x)$
$C'(2) = f'(g(2))~g'(2)$
$C'(2) = f'(1)~g'(2)$
$C'(2) = (3)(4)$
$C'(2) = 12$
