Solve the following problems, showing any necessary work. You must give EXACT answers, not decimal approximations (unless stated otherwise). 1. The Lambert W function w(x) is the inverse of the function f(x) = xe*. Use implicit differen- tiation to find w'(2e2). 2. Use logarithmic differentiation to find the derivative of (sin x + cos x) sin x-cos x 3. The curve C is defined by the implicit equation x2e2y - tan x arctany + x3 - y$ +1=0. Find an equation for the line tangent to C at the point (0, 1)