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The problem provided asks to find \((f - g)'(2)\) given some information about the functions \(f(x)\) and \(g(x)\) at \(x = 2\). Here's how we can solve it:

### Given:
- \( f(2) = 7 \)
- \( g(2) = 14 \)
- \( f'(2) = 12 \)
- \( g'(2) = 5 \)

### To find:
\[
(f - g)'(2)
\]

### Solution:
We can use the basic rule for differentiation:
\[
(f - g)'(x) = f'(x) - g'(x)
\]
At \(x = 2\), this becomes:
\[
(f - g)'(2) = f'(2) - g'(2)
\]

Substitute the given values:
\[
(f - g)'(2) = 12 - 5 = 7
\]

Thus, the answer is:
\[
(f - g)'(2) = 7
\]

Would you like further details or explanations?

Here are some related questions for you to consider:
1. How do you apply the sum/difference rule for derivatives in more complex functions?
2. What would \((f + g)'(2)\) be, using the same given data?
3. What happens to the derivative when functions are multiplied? (Product rule)
4. How does the chain rule apply to composite functions involving \(f\) and \(g\)?
5. Can you visualize the graphs of \(f(x)\) and \(g(x)\) based on this data?

**Tip**: Always verify if differentiation rules (sum, product, chain) are being correctly applied to avoid errors in more complex functions.

Misalkan fungsi f dan g terdiferensialkan di x = 2 dengan f(2) = 7, g(2) = 14, f'(2) = 12, dan g'(2) = 5. Tentukan (f - g)'(2).

Solve a problem where two functions f and g are given at x = 2, with their derivatives. Learn how to apply the subtraction rule of differentiation to find (f - g)'(2) with step-by-step guidance. This problem covers core calculus concepts suitable for students in Grades 10-12.

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