What is Differentiation in Mathematics?
Understanding the Basics
Differentiation is a fundamental concept in mathematics that involves finding the derivative or rate of change of a function.
Derivative as Instantaneous Rate of Change
The derivative of a function describes the function's instantaneous rate of change at a specific point. It provides the slope of the line tangent to the function at that point.
The Process of Differentiation
Differentiation is the process of finding the derivative of a function. It involves determining the instantaneous rate of change in the function based on one of its independent variables.
For example, the derivative of x2 is 2x, which means the slope of the tangent line to the function x2 at any point x is 2x.
Notations Used in Differentiation
In differentiation, we use the notation "dx" instead of "Δx" as the change in x approaches 0. The derivative of a function y with respect to x is commonly written as "dy/dx".
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