2. Rewrite as a sum or difference of multiples of logarithms. log - (x y z) log . (x y z) = 3. Differentiate the function. f(x) = = * - 1 + 11 f (x ) = 4. dy Find - ify = - - and u = 3 + 2t. uz + u dy 5. Differentiate. f(x) =x3 - 307% f (x ) = 6. Differentiate the following function. f(x)= xe 5x f '(x) = 7. Differentiate. y = dex + 6 dy dx 8. Differentiate. f(x) = 10 Inx f' (xx) = 9. Differentiate. In x y= dy dx 10. Differentiate. y = In (7x2 - 9x+1) y'= 11. Differentiate. f(x ) = In x4 - 10 X f(x) = 12. Find the equation of the line tangent to the graph of f(x) = (In x)? at x = B. y = (Type your answer in slope-intercept form. Do not round until the final answer. Then round to two decimal places as needed.)13. The demand for a new computer game can be modeled by p(x) = 55.5 -5 In x, for 0s xs 800, where p(x) is the price consumers will pay, in dollars, and x is the number of games sold, in thousands. Recall that total revenue is given by R(x) = x . p(x). Complete parts (a) through (c) below. a) Find R(x). R(X) = b) Find the marginal revenue, R (x)_ R (X)= c) How many units will be sold if the price that consumers are willing to pay is $40? The number of units that will be sold is (Round to the nearest whole number as needed.)14. Students in a zoology class took a final exam. They took equivalent forms of the exam at monthly intervals thereafter. After t months, the average score S(t), as a percentage, was found to be given by the following equation, where t 2 0. Complete parts (a) through (e) below. S(t) = 80 - 17 In (t + 1), Osts 80 a) What was the average score when they initially took the test? The average score was . (Round to one decimal place as needed.) b) What was the average score after 4 months? The average score after 4 months was . (Round to one decimal place as needed.) c) What was the average score after 24 months? The average score after 24 months was . (Round to one decimal place as needed.) d) Find S'(t). S'(t) = e) Find S'(4) and S'(24), and interpret the meaning of these numbers. S'(4) = . which means that after 4 months, the average score is (1) by points a month and S (24) = which means that after 24 months, the average score is (2) by points a month. (Type integers or decimals.) (1) O increasing (2) O decreasing O decreasing _ increasing