8. Given the function f (x) = (e*)(In x)(x), find f'(x) and simplify. (6pts) 9. Use logarithmic differentiation to find - dy if y = x * (8pts) dx 10. Find the equation of the tangent line to the curve y = (x +1)* at the point x = 1. (6pts) 1 1. Use the information in the table to answer the questions that follow: (12 pts) X 0 1 2 f(x) 1 3 2 g(x) -1/2 2 1 f (x) 5 -1/3 3 g (x) 1/3 -8/3 1/4 a. Find S'(2), if S(x) = ef(8(x) b. Find M'(0), if M(x) = In(f(x)g(x)) 12. Given that f'(x) = * - 3x-4 is the derivative for f (x), find the following: (12pts) (x - 5)2 a. The values of X, where there may be horizontal tangent lines. b. The values of X, where there may be vertical tangent lines. 13. The position function of the object is defined as s(t) = -4.9t + 120t, where s(t) is measured in meters above the ground and time is measured in seconds.(18 pts) a. What is the position of the object when t = 4 seconds? b. What's the average velocity during the first 10 seconds? c. What's the instantaneous velocity when t = 10 seconds? d. What's the instantaneous acceleration when t = 5 seconds? e. When is the velocity increasing? f. When is the object speeding up ?14. Consider the functions f (x) and g (x ) whose graphs are given below. (8 pts) (-4, 5) y = f(x) (1, 2) (6, 4) (-1, 2) (1, 1) - 2 2 4 6 X -2+ (5, -2) (-4, -3) y = 8(x) a. Suppose h(x) = Ing(x), Find h'(5) b. Suppose m(x) = 27(*), Find m'(-4)