1. (3 points) Consider the function a) Simplify f(x) and then determine f'(x). b) Without computing the f'(x) again, explain what general steps you would take to find f'(x) if you did not first simplify f(x). c) Which approach seems preferable, first simplifying the function then differentiating it, or differentiating first and then simplifying? 2. a) (2 point) Use the quotient rule to determine the derivatives of: tan(x) sec(x) b) (2 points) Find the equation of the tangent line to the graph of y = tan(x) sec(x) at x=. I 3. (3 points) Use the table below to evaluate the derivative H'(4), where H(): g(x)f(x) f(4) f'(4) g(4) g'(4) 10 -2 5 -1 Note that the notation f'(a) means evaluate the derivative function f'(r) at ra. This is very different than evaluating f(x) at a and then taking the derivative. The latter approach is always 0 and usually is not meaningful.