Standard Notation and Terminology
Key Questions

#d/dx# represents the derivative with respect to#x# .
So, the first derivative is
#y'={dy}/{dx}#
the second derivative is
#y''=d/{dx}(dy/dx)={d^2y}/dx^2# ,
and so on.
Questions
Derivatives

Tangent Line to a Curve

Normal Line to a Tangent

Slope of a Curve at a Point

Average Velocity

Instantaneous Velocity

Limit Definition of Derivative

First Principles Example 1: x²

First Principles Example 2: x³

First Principles Example 3: square root of x

Standard Notation and Terminology

Differentiable vs. Nondifferentiable Functions

Rate of Change of a Function

Average Rate of Change Over an Interval

Instantaneous Rate of Change at a Point