3. Let h(x) = g( f (x)). Use the graphs of f (x) and g(x) below to nd the indicated values of h'(x). (a) h '(2) (b) h '(0) - l at) 4. Suppose that the equation of motion of a particle is given by s(t) = A cos(ax + (5') , where a) and 6 are some constants. Under these circumstances, the particle is said to be under simple harmonic motion. (a) Find the velocity of the panicle at time t. (b) At what value(s) of t is the velocity of the particle 0? 5. Find each of the following derivatives: (a) [csc (x* ) ] (@ ) any [cos( e" ) . sin (w ) ] (d) a Jcor ( ( 3/ + 2 ) " )Section 3.7 Activity - The Chain Rule 1. Complete the rule: If h(x) = (f . g) (x) = f(g(x)), then h'(x) = Using Leibniz notation: Let z = g(x) and y = f(g(x)) = f(z) , then y' = _ dy dx 2. Given the table below, find h '(4) of each of the given functions. X 2 3 + f (x) w A 5 2 g (x) N f'(x) U N W 4 A W g'(x) 2 (a) h(x) = f(g(x)) (b) h ( x ) = g(f ( x ) ) (c) h(x) = g(8(x)) (d) h(x) = Vf(x) ( e ) h( x ) = = [(f - 8)()] (f) h( x) = Vx. f(Vx )