Calca — Foundations of Limits and Continuity + 4 more topics

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A derivative, at its heart, is about instantaneous rate of change. Think of it as finding the slope of a tangent line to a curve at a very specific point. Instead of calculating the average speed over an hour, a derivative helps you find your exact speed at 3:17 PM.

We often write the derivative of a function f(x) as f'(x) (read as "f prime of x") or dy/dx if y = f(x).

Derivatives are incredibly powerful for solving real-world problems. Most often, you'll encounter two main types of applications: optimization (finding maximums or minimums) and related rates (figuring out how different changing quantities affect each other).

When you're trying to understand what a function is doing, derivatives are your best friends. They give you a local look at how the function's output changes as its input changes.

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