If `f(x)=x+2," then "f'(f(x))" at "x=4`, is

Options

A. 8
B. 1
C. 4
D. 5

Answer

To solve the problem, we need to find \( f'(f(x)) \) at \( x = 4 \) given that \( f(x) = x + 2 \).

### Step-by-step Solution:

1. **Define the function**:
\[ f(x) = x + 2 \]

2. **Differentiate \( f(x) \)**:
To find \( f'(x) \), we differentiate \( f(x) \) with respect to \( x \):
\[ f'(x) = \frac{d}{dx}(x + 2) = 1 \]
Here, the derivative of \( x \) is \( 1 \) and the derivative of a constant \( 2 \) is \( 0 \).

3. **Evaluate \( f(x) \) at \( x = 4 \)**:
Now, we need to find \( f(4) \):
\[ f(4) = 4 + 2 = 6 \]

4. **Find \( f'(f(x)) \)**:
Since \( f'(x) = 1 \) for all \( x \), we can substitute \( f(x) \) into \( f' \):
\[ f'(f(x)) = f'(6) = 1 \]

5. **Final answer**:
Therefore, \( f'(f(x)) \) at \( x = 4 \) is:
\[ \boxed{1} \]