Preview Activity 2.5.1.
For each function given below, identify its fundamental algebraic structure. In particular, is the given function a sum, product, quotient, or composition of basic functions? If the function is a composition of basic functions, state a formula for the inner function \(g\) and the outer function \(f\) so that the overall composite function can be written in the form \(f(g(x))\text{.}\) If the function is a sum, product, or quotient of basic functions, use the appropriate rule to determine its derivative.
(a)
\(h(x) = \tan(2^x)\)
(b)
\(p(x) = 2^x \tan(x)\)
(c)
\(r(x) = (\tan(x))^2\)
(d)
\(m(x) = e^{\tan(x)}\)
(e)
\(w(x) = \sqrt{x} + \tan(x)\)
(f)
\(z(x) = \sqrt{\tan(x)}\)
