Part a: (3 points) Part b: (4 points) Part c: (3 points) Part d: (4 points) Determine the derivative of each of the following functions e* sin(z) 2 cos(z) In (In x)) 1+ 2. (4 points) Let f(x)=e* + sin(r) for x>-1. Note that f(0) = 1. Determine (f )'(1). 3. (3 points) If W denotes the weight (in pounds) of an individual, and t denotes the time (in weeks), then is the rate of weight gain of loss (in lb/wk). Suppose that a person weighted 220 pounds 10 weeks ago, and now weights 198 pounds. Using the Mean Value Theorem, show that their rate of weight loss must have exceeded 21bs/wk at some point during this 10 week period. 5. Consider the curve defined by Determine for this curve at the point (4,3). xy + y = 21