Tutorial Exercise Let f(x) = e*g(x), where g(0) = 4 and g'(0) = 3. Find f'(0). Step 1 We are given the function f(x) = e* g(x). The first step is to find the derivative f'(x). Let h(x) = e*, and note that the function f(x) is the product of the differentiable functions h(x) and g(x). Recall the product rule in terms of two differentiable functions h(x) and g(x). d dx P'(x) = h(x) [9'cx»] + g(x) [n'cx»)] To apply this rule, we first find the derivative of h(x) = e*. h(x) = e* h'(x) We now apply the product rule. P'M) = h(x) [9°x)] + g(x) (n'cx)]| f'(x) + g(x)

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