3.1: Derivative Formulas for Powers and Polynomials.

Main Points
The derivative of a constant is always 0 as it is simply a horizontal line and the slope of a linear function (a non-horizontal line) is always constant. When a constant, c, multiples a function, the derivative is: cf '(x). The derivative of a sum or difference is the sum or difference of each functions derivative respectively. The power rule of derivatives is: d/dx(x^n) = nx^n-1. To differentiate polynomial, the same rules for the sum, constant and powers apply. The derivative of a function using formulas would always give the function of the tangent at a point.

Challenges
The differences between the two methods used in obtaining a derivative are large. how was the connection between the two discovered? Because the honestly the derivative using the formula is very simple.

Reflections
Starting with lessons with learning to get derivatives by calculating the slope of the point in questions over smaller and smaller intervals does a lot with explaing just how differentiation works and what exactly it is and what it is meant for.