## Calculus: Early Transcendentals 8th Edition

(a) -2 (b) $-\frac{3}{8}$ (c) 6
$f(x)$ 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) $C(x) = f(g(x))$ $C'(x) = f'(g(x))~g'(x)$ $C'(2) = f'(g(2))~g'(2)$ $C'(2) = f'(4)~g'(2)$ $C'(2) = (3)(2)$ $C'(2) = 6$