You must show work. Partial or full credit will only be given if answers are supported by work. Also, if you have the correct answer but incorrect work to support the answer you will not receive full credit. 1. Find the derivatives of the following functions. Do not simplify. a. y = In x + In 2 (2 pts) b. y = 4ex (2 pts) C. y = 22* (2 pts) 2. Find h'(4) given g(4) = 6 and g'(4) = 3: (6 pts) h(x) = x g(x) 3. Find the derivatives of the following functions and simplify. a. f(x) = 10xe 5x (5 pts) b. f(x) = 5x(3x - 8)4 (6 pts)C. y = 6x - 2 (6 pts) 4x + 7 4. Find the derivative for the following functions and simplify. a. y = In (8x) (3 pts) b. y = log x (2 pts) C. y = 5x2 (In x) (5 pts) 5. Find the equation of the tangent line to the graph of (6 pts) y = (x - 7) In x atx = 7.6. Given f(x) = v(5x3 - 5x) , find the derivative of f and the values of x where the tangent line is horizontal. (5 pts) 7. The total cost (in hundreds of dollars) of producing x cameras per week is C(x) = 2 + v(5x + 9) Find C'(8) and interpret the result. (6 pts) 8. Use implicit differentiation to find dy/dx. (6 pts) xy + ey = 49. Price-Supply equation: Suppose the number x of coffee makers a retail chain is willing to sell per week at a price of $p is given by x =_100p where p E [20, 70]. 0. 1p + 1 Find the instantaneous rate of change of supply with respect to price when the price is $42. Interpret this result. (6 pts) 10. Price-demand equation: The number x of fitness watches that people are willing to buy per week from an online retailer at a price of $p is given by (6 pts) x = 3750 - 0.25p2 Use implicit differentiation to find dp/dx.11. A retail store estimates that weekly sales s and weekly advertising costs x (both in dollars) are related by S = 40000 - 25000e- 0005k The current weekly advertising costs are $2300 and these costs are increasing at the rate of $280 per week. Find the current rate of change of sales. (8 pts) 12. Given the following cost and revenue functions, where production is increasing at the rate of 375 calculators per week at a production level of 1600 calculators, find the rate of change in the profit with respect to time. (8 pts) C = 70000 + 50x and R = 200x - x2 30