```ad-note title: Definition The instantaneous rate of change of some variable $y$ with respect to $x$ at $x_1$ is the slope of the [[Tangent Line|tangent line]] to the curve at $y = f(x)$ at $P(x_1, f(x_1))$. $ \text{Instantaneous Rate of Change} = \lim_{\Delta x \to 0}{\frac{\Delta y}{\Delta x}} = \lim_{x_2 \to x_1}{\frac{f(x_2) - f(x_1)}{x_2 - x_1}} $ ```