Derivatives using tables Let h(x)=f(g(x)) and p(x)=g(f(x)). Use the table to compute the following derivatives. <IMAGE> b.
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Identify that h(x) = f(g(x)) is a composition of functions, which requires the use of the chain rule to find its derivative.
Recall the chain rule: if h(x) = f(g(x)), then h'(x) = f'(g(x)) * g'(x).
To find h'(2), substitute x = 2 into the derivative expression: h'(2) = f'(g(2)) * g'(2).
Use the table to find the values of g(2) and g'(2). Substitute these values into the expression.
Next, use the table to find f'(g(2)) by first finding g(2) and then using this result to find f' at that point. Substitute this value into the expression to complete the calculation of h'(2).
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