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: