Question

Let f(x) = In (In(x)). Find the value of f'(e).

Answer 1

To find the value of f'(e), we can differentiate the function f(x) = ln(ln(x)) using the chain rule.

The derivative of f(x) is given by f'(x) = 1/(ln(x) * x).

Now, we can substitute x = e into the derivative:

• f'(e) = 1/(ln(e) * e).

Since ln(e) = 1, we can simplify further:

f'(e) = 1/(1 * e) = 1/e.

Therefore, the value of f'(e) is 1/e.