Derivatives
Comprehensive introduction to derivatives, covering definitions, rules, rates of change, and applications in calculus.
Defining derivatives, derivative functions, differentiation rules, chain rule, implicit differentiation, trigonometric, exponential, logarithmic applications.
Tangent Lines
The Derivative of a Function at a Point
Velocities and Rates of Change
Derivative Functions
Graphing a Derivative
Derivatives and Continuity
Higher-Order Derivatives
The Basic Rules
The Power Rule
The Sum, Difference, and Constant Multiple Rules
The Product Rule
The Quotient Rule
Combining Differentiation Rules
Amount of Change Formula
Motion along a Line
Population Change
Changes in Cost and Revenue
Derivatives of the Sine and Cosine Functions
Derivatives of Other Trigonometric Functions
Higher-Order Derivatives
Deriving the Chain Rule
The Chain and Power Rules Combined
Combining the Chain Rule with Other Rules
Composites of Three or More Functions
The Chain Rule Using Leibniz’s Notation
The Derivative of an Inverse Function
Derivatives of Inverse Trigonometric Functions
Implicit Differentiation
Finding Tangent Lines Implicitly
Derivative of the Exponential Function
Derivative of the Logarithmic Function
Logarithmic Differentiation