Using the product rule and chain rule, we can find the derivative of y with respect to x as follows:
y = x^4sec(x^9)
y' = (4x^3)(sec(x^9)) + (x^4)(sec(x^9))(d/dx(tan(x^9)))
We can simplify the derivative using the identity d/dx(tan(u)) = sec^2(u)(du/dx), where u = x^9:
y' = (4x^3)(sec(x^9)) + (x^4)(sec(x^9))(sec^2(x^9))(9x^8)
Simplifying further, we get:
y' = 4x^3sec(x^9) + 9x^12sec(x^9)
Therefore, the derivative of y with respect to x is 4x^3sec(x^9) + 9x^12sec(x^9).