h(x)=\\sec ^{2}(4 x)\nwhich sequence of rules can be used in order to differentiate h\nin its current…

Explanation:

Step1: Analyze the function structure

The function (h(x)=\sec^{2}(4x)) can be seen as a composition of functions. Let (u = 4x), and (y=\sec^{2}(u)) (where (y = v^{2}) and (v=\sec(u))).

Step2: Apply the chain - rule concept

The chain - rule states that if (y = f(g(x))), then (y^\prime=f^\prime(g(x))\cdot g^\prime(x)). For (y = v^{2}) with (v=\sec(u)) and (u = 4x), first, when differentiating (y) with respect to (v) ((\frac{dy}{dv}=2v)), then differentiating (v) with respect to (u) ((\frac{dv}{du}=\sec(u)\tan(u))), and finally differentiating (u) with respect to (x) ((\frac{du}{dx}=4)). We use the chain - rule twice. First, for (y = v^{2}) (where (v) is a function of (u)) and then for (v=\sec(u)) (where (u) is a function of (x)).

Answer:

D. Chain rule, then chain rule again