Welcome to Calculus: Understanding Derivatives 🎓
Introduction to Derivatives
Derivatives represent how a function changes as its input changes. Formally, the derivative of a function f at a point x is given by the limit:
f'(x) = lim(h→0) [(f(x + h) - f(x)) / h]
This represents the slope of the tangent line to the curve of the function at any given point.
Why Are Derivatives Important?
Derivatives are fundamental in physics, engineering, economics, and beyond. They allow us to understand rates of change, optimization problems, and provide a foundation for further calculus concepts.
Graphical Interpretation
Visualize a curve on a graph. The derivative at a certain point is the slope of the tangent to the curve at that point.
Further Reading
Calculus with a little froge flare! 🐸
