If `f(0)=0,f^(prime)(0)=2,` then the derivative of `y=f(f(f(x)))` at `x=0` is 2 (b) 8 (c) 16 (d) 4

Options

A. 2
B. 8
C. 16
D. 4

Explanation

To find the derivative of \( y = f(f(f(x))) \) at \( x = 0 \) given that \( f(0) = 0 \) and \( f'(0) = 2 \), we will use the chain rule for differentiation.

### Step-by-step solution:

1. **Differentiate \( y = f(f(f(x))) \)**:
Using the chain rule, we differentiate \( y \) with respect to \( x \):
\[
\frac{dy}{dx} = f'(f(f(x))) \cdot f'(f(x)) \cdot f'(x)
...