Definition+of+the+derivative+of+a+function

=﻿__Definition of the Derivative of a Function__=

//What is the Derivative?//
The Derivative of a function is the equation that will give you the slope of the tangent line at any point along a given curve. In other words, the Derivative allows you to analyze the rate of change of a function at any instant along the curve.

//﻿Mathematical Definition of the Derivative//
Let a given curve be defined as y = f(x). The derivative of this function will be denoted as f '(x), "f prime of x."

** Example One **
Find the Derivative of the function: f(x)=3x+2

//**Tangent Lines**//
The derivative can be used to write the equations of special lines called Tangent Lines. These lines give a graphical representation of the slope of a curve at a given point.

**Example Two** Find the equation of the tangent line of f(x)=x 2 +2 at x=1.

Solution: