To explain how to find the derivative of \( g(x) \), I'll outline the general steps:

1. **Identify the Function \( g(x) \):**  
   The first step is knowing the exact form of the function \( g(x) \). Derivatives depend on the function's composition (whether it's a polynomial, exponential, logarithmic, etc.).

2. **Apply the Appropriate Differentiation Rule:**
   Based on the structure of \( g(x) \), different rules for differentiation can be applied. Here are the most common rules:
   - **Power Rule**: If \( g(x) = x^n \), then \( g'(x) = n \cdot x^{n-1} \).
   - **Product Rule**: If \( g(x) = u(x) \cdot v(x) \), then \( g'(x) = u'(x) \cdot v(x) + u(x) \cdot v'(x) \).
   - **Quotient Rule**: If \( g(x) = \frac{u(x)}{v(x)} \), then \( g'(x) = \frac{u'(x) v(x) - u(x) v'(x)}{(v(x))^2} \).
   - **Chain Rule**: If \( g(x) = f(h(x)) \), then \( g'(x) = f'(h(x)) \cdot h'(x) \).

3. **Differentiate Term by Term:**
   For functions made up of multiple terms, apply the differentiation rules to each term separately. Combine the results to get the final derivative.

4. **Simplify the Result:**
   After applying the differentiation rules, simplify the resulting expression as much as possible.

5. **Check for Special Cases:**
   If \( g(x) \) involves more complex functions (e.g., trigonometric, exponential, or logarithmic functions), specific rules for those functions may need to be used.

If you provide me with the specific function \( g(x) \), I can walk you through the exact steps to differentiate it.

Would you like more details or have any specific questions about this process?

Here are 5 related questions you might find helpful:

1. What is the derivative of \( g(x) = \sin(x) \)?
2. How do you apply the product rule to \( g(x) = x^2 \cdot e^x \)?
3. Can you find the derivative of \( g(x) = \ln(x) \)?
4. What is the chain rule, and how is it used in derivatives?
5. How do you differentiate implicit functions?

**Tip:** Always remember to simplify the derivative after applying the rules to avoid unnecessary complexity in your answer.

Learn how to find the derivative of g(x) using key differentiation rules such as the Power Rule, Product Rule, Quotient Rule, and Chain Rule. This solution provides a comprehensive guide for calculus students in Grades 11-12.

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