It seems like you're asking about a function \( f(x) \), but the formatting might need clarification. From what I can gather, you might be defining a piecewise function or simply combining terms. 

Here are two possible interpretations:

### 1. If you mean the function is a sum of two terms:
\[ f(x) = 7 + \ln(x) \]
In this case, the function consists of a constant term (7) and a logarithmic term (the natural logarithm of \(x\)).

### 2. If you mean the function has a piecewise definition:
\[ f(x) = 
\begin{cases} 
7 & \text{if } x \text{ is some specific range,}\\
\ln(x) & \text{otherwise.}
\end{cases}
\]

If it's the first case (a sum), the derivative of \( f(x) = 7 + \ln(x) \) with respect to \( x \) is:
\[
f'(x) = 0 + \frac{1}{x} = \frac{1}{x}
\]
And the integral would be:
\[
\int (7 + \ln(x)) \, dx = 7x + x\ln(x) - x + C
\]

Could you confirm if one of these interpretations is correct? Feel free to clarify or ask further questions!

### Related Questions:
1. How do we interpret logarithmic functions in terms of their graphs?
2. What are the properties of the natural logarithm function?
3. How do constants affect the behavior of functions?
4. What happens to the function \( f(x) = \ln(x) \) as \( x \to 0 \)?
5. How does the derivative of \( \ln(x) \) behave for different values of \( x \)?

**Tip**: Remember, the domain of \( \ln(x) \) is \( x > 0 \), so \( f(x) = 7 + \ln(x) \) is only defined for positive \( x \).

Explore the derivative and integral of the function f(x) = 7 + ln(x), including step-by-step solutions using calculus concepts like logarithmic differentiation and the fundamental theorem of calculus. Suitable for Grades 11-12.

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