\( \underbrace{\begin{array}{c}\text { Chapter 12 } \\ \text { Derivatives }\end{array}} \)

Did you know that derivatives were first rigorously formulated in the late 17th century by mathematicians like Isaac Newton and Gottfried Wilhelm Leibniz? Their work laid the groundwork for calculus, revolutionizing not just mathematics but also physics and engineering. Both pioneers had a healthy rivalry, with Leibniz’s notation \( \frac{dy}{dx} \) still being used today, which certainly adds a spicy twist to the history of math! In today's world, derivatives play a crucial role beyond just theoretical math. For instance, they are used in economics to determine how responsive supply and demand are to price changes, a concept known as elasticity. In finance, derivatives can help assess risks and potential profits in markets, making them essential tools for investors and analysts alike. So the next time you're analyzing a stock, remember, derivatives are working their magic behind the scenes!