The following questions are a suggested list of practice problems to prepare for your test. These questions are not guaranteed to be a complete preparation for the exam, but they can serve as a starting point. You should also refer to your homework and extra worksheets provided by your professor. On the test, you WILL BE expected to fully support your answers using Calculus techniques taught in class. SHORT CUTS will not be accepted as supporting work, but should be used to check your answers only. Practice showing work in an organized, legible manner. 1. Calculate the following derivative. 10x5 - 4Inx -2+8ex - 1) 2. Find the derivative of the following function. a. y = _ 15-t2+2t-1 by = (x2 - 1)(x2 -3) c. y = (1 - secx)(1 + secx) 3. Find the derivative of the following function. a. y = x2 In x b. y = 02 tan 0 c. y = x3ex d. y = cos x sin x 4. Find the derivative of the following function. a. f (x) =- b. f ( x ) = = 7x 3 ex d. f (x) = cos x 3 secx c. f (x) = sin x 5. Find the first 4 derivatives of the following function. a. y = In(4 -5x) b. y = sin(2x) c. y = e-2x d. y = x3 - 2x 6. Find the derivative of the following functions. a. (tan(3x5)) b. - ((3x6 - 8x)?) C. ag (ecsco) d. (In(cos(2t))) e. dx (5x3-1)2 f. d d In ( 5 x3 ) h. y = x2+2 Vx(3x+1)NIH till. LBILUIU: A . . - d? 7. Use implicit differentiation to find 3;. c.1n)')'2+xy=o a. 4y+x3xy=3x :(y H - tan = 10.: b. y - ("05(ny = x d. y (3') 8. Find the tangent line to the curve: a. y = 21110: 3) at the point (4,0) b. y = e"Jr at the point (0,1) I:, y = i at the point {3.1} 9. A search and rescue airplane is flying in a circle with radius expanding at a rate of 3 mph. At what rate is the search area expanding when the radius is 12 miles? {Answers should be exact.) 10. A solid spherical ball is heated and begins to expand. At what rate is the radius increasing when the radius is 4 rn and the volume is increasing at a rate of 2 m'fsec? (Answers should be exact.) {Volume of a sphere is V 5 11TH.) 3 11. A 17-foot ladder is leaning against a wall when it begins to slide away from the wall. At what rate is the ladder sliding down the wall when the top of the ladder is at a height of 15 feet and the base of the ladder is slipping away from the wall at a rate of 5ftfsec? 12. Two trains leave a station. one headed due west and the other headed due south. How fast the is southern hound train moving if the west bound train is 2G miles from the station traveling at a constant speed of 23 mph, the distance between the trains is 25 miles, and the distance between them is increasing at a rate of 40 mph. [Round answer to nearest hundredth.) 13. Find% for the following equations. 3' y z (eosx)x b. y = .t:x c. y = x9" d. y = J