In calculus, a derivative is a measure of how a function changes over time. It is a fundamental tool of calculus and is used to study how functions change over time. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. In other words, derivatives provide information about the direction a function is moving at any given point. Derivatives are incredibly important because they allow individuals to study how functions change over time and have a wide range of applications in the real world, including in physics, engineering, and economics. Differentiation is the process of calculating the derivative of a function, and there are a few simple rules that can be used to calculate the derivatives of most functions.