To solve this problem we must apply the chain rule.
Chain rule tells us how to derive composite functions.
We have to use the formula:
[f(g(x))]' = f'(g(x)) . g'(x)
In other words we must identify two functions and apply the formula.
We can see that f(x) is the given function itself:
f(x) = (2x +1) ⁴
The g function must be
g(x) = 2x + 1
Let's derive separately .
f'(x) = 4.(2x + 1)³
Then
g'(x) = 2
Let's put everything together. We get:
f'(x) = 4.(2x + 1)³. 2
f'(x) = 8.(2x + 1)³
Answer: f'(x) = 8.(2x + 1)³