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4.3 and 4.4 - The (all important) General Power Rule or Chain Rule (A function h is a composite of functions f and g if h(x) f [g(x)] . The domain of m is the set of all numbers x such that x is in the domain of g, and g(x) is in the domain of f. ) Examples: function y f (x) = u(x) n (a) derivative y = f ( x) = n u (x) n 1 u( x) (Notice that we now have a function raised to a power and not just x raised to a power) (b) y = f ( x) = e u(x) (c) y = f (x) = ln u(x) , u(x)> 0 y = f ( x) = e u(x) u( x) y = f ( x) = (Again, notice that we now have functions raised to a function and not just x ) Examples: 1 u( x) u (x) 4.3 HW # 1 – 35 (odd) 4.4 HW # 1 - 49 (every other odd), 51 - 61 (odd), 71