Final answer:
Solve for dy/dx of the function y= sec^3(tan^2 3x), chain rule and implicit differentiation are used, involving two layers of differentiation.
Step-by-step explanation:
To find dy/dx for the function y= sec^3(tan^2 3x), we would use chain rule and implicit differentiation techniques. Since this task requires advanced calculus concepts, typically covered in high school or early college courses, it involves multiple layers of differentiation.
First, differentiate sec^3(u) with respect to u to get 3sec^2(u)sec(u)tan(u), then differentiate tan^2(3x) with respect to x to get 2tan(3x)(sec^2(3x))(3).