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Active Calculus 2nd Ed

Activity 2.5.2.
For each function given below, identify an inner function \(g\) and outer function \(f\) to write the function in the form \(f(g(x))\text{.}\) Determine \(f'(x)\text{,}\) \(g'(x)\text{,}\) and \(f'(g(x))\text{,}\) and then apply the chain rule to determine the derivative of the given function.
(b)
\(p(x) = \sqrt{ \tan(x) }\)
(e)
\(m(x) = (\sec(x) + e^x)^9\)