The Derivative
as a Function
Definition of Derivative Function
Differentiability
Continuity
Has Derivative
Rules for Constants, Powers,
Multiples, and Sums
Constant Function
Power Rule
Constant Multiple Rule
Derivative Sum Rule
One-Sided Derivatives
Intermediate Value Property of Derivatives
Second- and Higher-Order Derivatives
The Derivative as
a Rate of Change
Instantaneous Rate of Change
Velocity
Instantaneous
Average
Speed, Acceleration, Jerk
Derivatives of Products,
Quotients, and Negative Powers
Derivative Product Rule
Derivative Quotient Rule
Power Rule for Negative Integers
The Chain Rule and
Parametric Equations
The Chain Rule
Power Chain Rule
Slopes of Parametrized Curves
Implicit Differentiation
Definition: Implicit Differentiation
Four Steps
Differentiate both
sides of the equation
Collect the terms with dy/dx
on one side of the equation
Factor out dy/dx
Solve for dy/dx
Derivatives of Higher Order
Power Rule for
Rational Powers
Related Rates
Strategy
Draw a picture and name the
variables and constants.
Write down the numerical information
Write down what you're asked to find
Write an equation that relates the variables
Differentiate w.r.t. t
Evaluate
