Solve the following problems, showing any necessary work. You must give EXACT answers, not decimal approximations (unless stated otherwise). The Lambert W function w(x) is the inverse of the function f(x) = xex. Use implicit differen- tiatuon to find (2e2). Use logarithmic differentiation to find the derivative of (sin x + cos x) x The curve C is defined by the implicit equation x2e2y tanxarctany+x 1 = 0. Find an equation for the line tangent to C at the point (0, 1). 4. Use the values in the following chart to evaluate the quantities below. b. d. A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is I m higher than the bow of the boat. If the rope is pulled in at a rate of 2 rn/s, how fast is the boat approaching the dock when it is 18 m from the dock? Find the quantities dx, Ay, and dy, if y = 3x2 + x, x = l, and Ax = 0.2.