Question

Given \( f'(1) = 3 \), \( f(1) = 1 \), and
\[ y = f\left(f(f(x))\right) + \left(f(x)\right)^2, \] then find \( \frac{dy}{dx} \) at \( x = 1 \).

• A. \( 9 \)
• B. \( 12 \)
• C. \( 15 \)
• D. \( 18 \)

Hint:

When differentiating composite functions like \( f(f(f(x))) \), apply the chain rule multiple times step by step and plug in given values carefully.