If f(1) = 1, f'(1) = 3, then the derivative of f(f(x))) + `(f(x))^(2) ` at x = 1 is

Options

A. 15
B. 12
C. 9
D. 33

Explanation

To find the derivative of the function \( f(f(x)) + (f(x))^2 \) at \( x = 1 \), we will follow these steps:

### Step 1: Differentiate the function
We need to differentiate the function \( f(f(x)) + (f(x))^2 \) using the chain rule and the product rule.

The derivative of \( f(f(x)) \) is given by:
\[
\frac{d}{dx} f(f(x)) = f'(f(x)) \cdot f'(x)
...