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 $f(g(x))$. Determine $f'(x)$, $g'(x)$, and $f'(g(x))$, and then apply the chain rule to determine the derivative of the given function.

1. $h(x) = \cos(x^4)$

2. $p(x) = \sqrt{ \tan(x) }$

3. $s(x) = 2^{\sin(x)}$

4. $z(x) = \cot^5(x)$

5. $m(x) = (\sec(x) + e^x)^9$