Welcome to basic differentiation! Differentiation is one of the most important concepts in calculus. It helps us find the instantaneous rate of change of a function, which means how fast something is changing at a specific moment in time. Visually, differentiation gives us the slope of the tangent line to a curve at any point. Watch as this red tangent line changes its slope as we move along the blue curve.
Before we learn the rules of differentiation, let's understand the notation. The derivative of a function f of x can be written in three common ways. First, f prime of x, which uses an apostrophe. Second, dee y dee x, which looks like a fraction. Third, dee over dee x of f of x. All three notations represent exactly the same thing - the derivative. For example, if we have f of x equals x squared, then f prime of x, dee y dee x, and dee over dee x of x squared all equal 2x.