The difference quotient is $$ \square . \begin{array}{l}\frac{f(x+h)-f(x)}{h}\end{array} $$

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The difference quotient is a fundamental concept in calculus, particularly in the definition of the derivative. It is expressed as:

$$
\frac{f(x+h) - f(x)}{h}
$$

where:
- $$ f(x) $$ is a function,
- $$ h $$ is a small increment in $$ x $$,
- $$ x $$ is the point at which we are evaluating the function.

### Explanation of the Difference Quotient

1. **Function Evaluation**: The term $$ f(x+h) $$ represents the value of the function at the point $$ x+h $$, which is a small step away from $$ x $$.

2. **Function Value at $$ x $$**: The term $$ f(x) $$ is simply the value of the function at the point $$ x $$.

3. **Difference**: The expression $$ f(x+h) - f(x) $$ calculates the change in the function's value as $$ x $$ changes to $$ x+h $$.

4. **Average Rate of Change**: Dividing this difference by $$ h $$ gives the average rate of change of the function over the interval from $$ x $$ to $$ x+h $$.

5. **Limit Process**: As $$ h $$ approaches 0, the difference quotient approaches the derivative of the function at the point $$ x $$, which is defined as:

$$
f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}
$$

### Summary

The difference quotient is a way to measure how a function changes as its input changes. It is a crucial step in understanding derivatives and the concept of instantaneous rate of change.
The difference quotient is $$ \frac{f(x+h) - f(x)}{h} $$.

The difference quotient is \( \square . \begin{array}{l}\frac{f(x+h)-f(x)}{h}\end{array} \)

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