Average Marginal cost is

Options

A. `(d)/(dx)(AC)`
B. `(d)/(dx)(MC)`
C. `(MC)/(x)`
D. `(d)/(dx)(AC + MC)`

Answer

To solve the question "Average Marginal Cost is", we need to understand the relationship between average cost and marginal cost.

### Step-by-Step Solution:

1. **Understanding Average Cost (AC)**:
- Average Cost is defined as the total cost (TC) divided by the quantity of output (Q).
- Formula:
\[ AC = \frac{TC}{Q} \]

2. **Understanding Marginal Cost (MC)**:
- Marginal Cost is the additional cost incurred by producing one more unit of a good or service.
- It can be calculated as the change in total cost when the quantity produced is increased by one unit.
- Formula:
\[ MC = \frac{d(TC)}{dQ} \]

3. **Finding Average Marginal Cost**:
- Average Marginal Cost can be interpreted as the change in average cost with respect to the change in quantity produced.
- Mathematically, this can be represented as the derivative of the average cost with respect to quantity.
- Formula:
\[ \text{Average Marginal Cost} = \frac{d(AC)}{dQ} \]

4. **Relating Marginal Cost to Average Cost**:
- The relationship between marginal cost and average cost can be expressed as:
\[ MC = AC + Q \cdot \frac{d(AC)}{dQ} \]
- From this, we can derive that:
\[ \frac{d(AC)}{dQ} = \frac{MC - AC}{Q} \]

5. **Conclusion**:
- Thus, the average marginal cost is effectively the derivative of the average cost with respect to output quantity, which can be expressed as:
\[ \text{Average Marginal Cost} = \frac{d(AC)}{dQ} \]

### Final Answer:
The average marginal cost is given by the formula:
\[ \text{Average Marginal Cost} = \frac{d(AC)}{dQ} \]