The document outlines several basic rules and theorems for differentiation including definitions for differentiation, linearization, Leibniz' rule for repeated differentiation, standard inverse trigonometric derivatives, the intermediate value theorem, Rolle's theorem, the mean value theorem, and the constant difference theorem. Key concepts covered are definitions of continuity and differentiability, functions taking on values within a range, existence of critical points and points where the derivative is equal to the difference quotient, and conditions where the difference of derivatives is constant.

1. FACT SHEET:
BASIC RULES AND THEOREMS
FOR DIFFERENTIATION
Definition for Differentiation
Linearization
Leibniz’ Rule for Repeated Differentiation
Standard Inverse Trigonometric Derivatives
Intermediate Value Theorem
A function that is continuous at for all values of takes
on every value between .
Rolle’s Theorem
Given:
o is CONTINUOUS at all
o is DIFFERENTIABLE at all
o
Then:
Mean Value Theorem
Given:
o is CONTINUOUS at all
o is DIFFERENTIABLE at all
Then:
Constant Difference Theorem
If: at each …
Then: