Final answer:
The derivative of 4e to the 4x is 16e to the 4x.
Step-by-step explanation:
The derivative of 4e4x can be found using the chain rule.
The chain rule states that if you have a function g(x) = f(h(x)), then the derivative of g(x) is the derivative of f evaluated at h(x) times the derivative of h(x).
Applying the chain rule to 4e4x, we have:
g(x) = 4e4x
f(x) = eu (where u = 4x)
h(x) = 4x
Using the chain rule, we find:
g'(x) = f'(h(x)) * h'(x) = e4x * 4
Therefore, the derivative of 4e4x is 4e4x * 4, which simplifies to 16e4x.