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Differentiate the function y = sec(4x).

The derivative of y = sec(4x) is y' = 4sec(4x)tan(4x).

To differentiate y = sec(4x), we can use the chain rule. Let u = 4x, then y = sec(u). Using the chain rule, we have:

y' = sec(u)tan(u)u'

where u' is the derivative of u with respect to x. In this case, u' = 4.

Substituting back in for u, we have:

y' = sec(4x)tan(4x)(4)

Simplifying, we get:

y' = 4sec(4x)tan(4x)

Therefore, the derivative of y = sec(4x) is y' = 4sec(4x)tan(4x).

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