1. Let g(x) be a differentiable function which is always positive (i.e., g(x) > 0 for all x in its domain), let h(x) be a differentiable function, and set f(x) = g(x)"(2). (We need g(x) > 0 so that taking arbitrary exponents makes sense.) Q: How do we compute the derivative of f? We know the answer already in two cases : If g(x) is a constant, say g(x) = b, then f(x) = b(2), which we know how to differentiate by combining the chain rule and the rule for differentiating b. On the other hand, if h(x) is a constant, say h(x) = r, then f(x) = g(x)", which we know how to differentiate by combining the chain rule and the rule for differentiating x for arbitrary r ER. To get the rule for differentiating x" we used the method of logarithmic differentiation, and that method also lets us compute the deriviative of arbitrary f of the form g(x) "(2). In this problem we will practice that method. Let f(x) = (1 + 22) cos(x) . (a) Write out In(f (x)), and simplify using the rules for logarithms. (b) Differentiate In(f (x)), and the simplification in (a), and then solve to find the formula for f'(x). Apply this method to compute the derivatives below. (c) d (3 + sin(x) ) (ez2 ) (d) d (2" + 3x4) (Ina)