You may not use notes or a calculator on this exam. In order to receive credit. organized fashion using correct notation. Do all of your work on separate paper. Good Luck! 1) CHOOSE 5. Clearly identify the 5 you have chosen. Find the derivative of each function. Show all work in neatly organized steps. Answers must be in simplest form. Do not leave negative exponents or fractional exponents in final answers. No extra credit will be given for doing a sixth problem. fax)=4x-1 1)/(x)=-2ex b) f(x)= cos(3x) e) f(x) = (6-5x) (4 points each) f(x) = In (sinx) 1)f(x)=62x 2) Find and the equation of the line tangent to the graph of x + 2xy-3y = -12 at (0,2). (10 points) 3) Use logarithmic differentiation to find y = (x-1). (No credit will be given if the Quotient Rule is used in place of logarithmic differentiation.) (10 points) 4) CHOOSE 5: Clearly identify the 5 you have chosen. Find the derivative of each function. Show all work in neatly organized steps. Answers must be in simplest factored form. Rationalizing denominators is not required. Do not leave (6 points each) negative exponents in final answers. Do not use logarithmic differentiation. No extra credit will be given for doing a sixth problem. (2x+5)2 a) f(x) = (x-1)4 d) f(x)=tan(5x) b) f(x) = (sinx) (e cosx) e) (x) = = In 2x-1 e3x c)(x) = cot (sinx) f) f(x) = (ex + 4)(4- e*) 5) 16) 5) CHOOSE 2 of the following problems. Clearly identify the two that you have chosen. Draw and label a diagram to represent the problem. Answer must be in simplest form. No extra credit will be given for doing a second problem. Explain your solution in a sentence, including whether the change is an increase or decrease. (10 points each A balloon rises vertically at a rate of 3 feet per second from a point on the ground which is 50 feet from an observer. Find the rate of change of the angle of elevation by the point on the ground where the observer is standing and the balloon, when the balloon is at a height of 120 feet. D b) A spherical balloon is inflated at a rate of 400 cubic centimeters per minute. How fast is the radius of the balloon changing at the instant that the radius is 10 centimeters? Leave the answer in terms of . (Volume sphere: CA balloon is at a height of 33 feet and rising at a rate of 1 foot per second when a bike passes directly it, traveling at a rate of 9 feet per second. What is the rate of change of the distance between the bike balloon, 3 seconds later? A CREDIT: (4 points - no partial credit) Find the second derivative of x + y = 36, in simplest form.