Yes, you are describing the definition of the derivative of a function $f(x)$. Formally, the derivative $f'(x)$ is defined as the limit:

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

This formula represents the instantaneous rate of change of the function $f(x)$ at any point $x$. Here’s a breakdown of what each part means:

1. $f(x+h)$: The value of the function at a point slightly offset from $x$ by an amount $h$.
2. $f(x+h) - f(x)$: The change in the function’s value over the interval $[x, x+h]$.
3. $\frac{f(x+h) - f(x)}{h}$: This is the difference quotient, which approximates the slope of the secant line between the points $(x, f(x))$ and $(x+h, f(x+h))$.
4. $\lim_{h \to 0}$: As the interval $h$ shrinks to 0, the difference quotient approaches the slope of the tangent line to the curve at $x$, which is the derivative.

Thus, the derivative provides the slope of the tangent line to the curve at a specific point $x$, giving the rate at which $f(x)$ is changing with respect to $x$.

Would you like a more detailed explanation of this concept or examples to clarify it further?

Here are 5 related questions:

1. How does the derivative relate to the concept of velocity in physics?
2. Can a function have points where the derivative does not exist?
3. What is the geometric interpretation of a derivative at a point?
4. How do higher-order derivatives (like $f''(x)$) differ from the first derivative?
5. What is the relationship between differentiability and continuity?

Tip: Always check the limit process when calculating a derivative. Understanding how small changes in $h$ affect the function can help avoid common mistakes.