If f (x)=x+7 , and g (x)=x-7 , x `in` R , then `d/(dx)` (gof)(x)=_____

Answer

To solve the problem, we need to find the derivative of the composition of two functions \( g(f(x)) \), where \( f(x) = x + 7 \) and \( g(x) = x - 7 \).

### Step-by-Step Solution:

1. **Identify the Functions**:
We have:
\[ f(x) = x + 7 \]
\[ g(x) = x - 7 \]

2. **Find the Composition \( g(f(x)) \)**:
To find \( g(f(x)) \), we substitute \( f(x) \) into \( g(x) \):
\[ g(f(x)) = g(x + 7) \]
Now, replace \( x \) in \( g(x) \) with \( f(x) \):
\[ g(x + 7) = (x + 7) - 7 \]
Simplifying this gives:
\[ g(f(x)) = x + 7 - 7 = x \]

3. **Differentiate \( g(f(x)) \)**:
Now, we need to differentiate \( g(f(x)) \):
\[ \frac{d}{dx}(g(f(x))) = \frac{d}{dx}(x) \]
The derivative of \( x \) with respect to \( x \) is:
\[ \frac{d}{dx}(x) = 1 \]

4. **Final Answer**:
Thus, the derivative \( \frac{d}{dx}(g(f(x))) \) is:
\[ \boxed{1} \]