Proving facts about the derivatives of vector functions including the product rule

Using the limit definition to find derivatives of functions and vector functions

Using the limit definition to find a derivative and proving the power rule

Proving the Product Rule and the rule for the derivative of a difference of functions

Proving the derivatives of trigonometric functions and that sine is continuous

Proving Fermat's Theorem and graphing local and absolute extrema

Using the Mean Value Theorem to prove facts about functions

Proving and then applying the Fundamental Theorem of Calculus

Using L'Hospital's Rule to evaluate a limit representing a derivative at a point