Using derivative for velocity

Use the derivative to find the instantaneous velocity of a function.

Solving with the derivative

Some different problems using the derivative.

Trigonometric derivatives

Proof of trigonometric derivatives using the Limit Definition of the Derivative.

Techniques of Differentiation

Proofs for the product rule and quotient rule when finding the derivative.

Increments and Differentials

Solving problems with the derivative and increments of x, involving linear approximation.

The Chain Rule

Solving derivatives using the chain rule.

Finding Tangent Lines

Solving for equations of tangent lines involving specific points on a graph.

Derivative Problems

Some word problems involving rates and derivatives.

Vertical Tangent Lines

Finding vertical tangent lines of a function.

Related Rates

Related rate problems.

The Mean Value Theorem

Rolle's theorem and the Mean value theorem (MVT).

Optimization

Applications of the derivative to optimize functions.

Graphing Guidelines

Graphing guidelines using first derivative test and concavity test (aka second derivative test).