Derivatives
Start your calculus journey here by measuring how fast things change.
Visualizing Change
Constant Rate of Change
Variable Rate of Change
Average Rate of Change
Secant Lines
Average Change of Functions
Level Review
Net Change
Negative Rate of Change
Displacement
Velocity
Difference Quotients
Level Review
Local Linearity
The Tangent Line
The Derivative
Instantaneous Velocity
Undefined Derivatives
Level Review
The Limit Definition of Derivative
Interpreting Limits as Derivatives
Derivative Notation
Level Review
Computing Derivatives for f(x) = x²
The Derivative Function of f(x) = x²
Derivatives of Linear Functions
The Derivative of f(x) = 2ᕽ
Derivatives of Exponential Functions
Derivative of the Square Root Function
Linear Approximation
Level Review
Graphing the Derivative
Position from Velocity
Derivatives of Quadratics
Exponential Growth and Decay
Local Extrema
Interpreting the Derivative
Level Review
Derivatives of Powers
The Power Rule
The Constant Multiple Rule
The Sum Rule
Derivatives of Polynomials
Level Review
Periodic Motion
The Slope of Sine
The Derivative of Sine
The Slope of Cosine
The Derivative of Cosine
Amplitude and Offset
Frequency and Velocity
Level Review
Growing Squares
(Coming soon)
Growing Circles
(Coming soon)
Growing Rectangles
(Coming soon)
Products of Functions
(Coming soon)
The Product Rule
(Coming soon)
Proving the Product Rule
(Coming soon)
Using the Product Rule
(Coming soon)
Products of Polynomials
(Coming soon)
More than Two Functions
(Coming soon)
Powers of Functions
(Coming soon)
Product Rule Challenge
(Coming soon)
Reciprocal Powers
(Coming soon)
Reciprocal Functions
(Coming soon)
The Quotient Rule
(Coming soon)
Applying the Quotient Rule
(Coming soon)
The Derivative of Tangent
(Coming soon)
Quotients at a Point
(Coming soon)
Derivatives of Dilations
(Coming soon)
Changing time units
(Coming soon)
Why Rates Multiply
(Coming soon)
The Chain Rule
(Coming soon)
The derivative of a composition
(Coming soon)
Proof of the Chain Rule
(Coming soon)
Practicing the Chain Rule
(Coming soon)
The Natural Logarithm
(Coming soon)
Derivative of Natural Log
(Coming soon)
Derivatives of Fractional Exponents
(Coming soon)
Radical Expressions
(Coming soon)
Derivatives of Inverse Trig Functions
(Coming soon)
Derivative of Inverse Functions
(Coming soon)
Derivative of General Exponentials
(Coming soon)
L'Hôpital's Rule
(Coming soon)
Proving L'Hôpital
(Coming soon)
Applications of L'Hôpital
(Coming soon)
L'Hôpital and 0⋅∞
(Coming soon)
L'Hôpital and ∞ - ∞
(Coming soon)
L'Hôpital and ∞/∞
(Coming soon)
L'Hôpital and Exponents
(Coming soon)
The Circle
(Coming soon)
The Circle Revisited
(Coming soon)
Derivatives of Curves
(Coming soon)
The Rational Power Rule
(Coming soon)
Horizontal and Vertical Tangents
(Coming soon)
Squashing a Square
(Coming soon)
A Sliding Ladder
(Coming soon)
A Rocket Launch
(Coming soon)
Growing Shadows
(Coming soon)
A Cylindrical Tank
(Coming soon)
A Conical Tank
(Coming soon)
Concavity
(Coming soon)
The Second Derivative
(Coming soon)
Graphing the Second Derivative
(Coming soon)
Interpreting The Second Derivative
(Coming soon)
Concavity of Curves
(Coming soon)
Higher Derivatives
(Coming soon)
The First Derivative Test
(Coming soon)
Applications of The First Derivative Test
(Coming soon)
The Second Derivative Test
(Coming soon)
The Extreme Value Theorem
(Coming soon)
Applications of Optimization
(Coming soon)
Rolle's Theorem
(Coming soon)
The Mean Value Theorem
(Coming soon)
Mean Values in Context
(Coming soon)
Mean Values and Root Finding
(Coming soon)
Existence of The Derivative
(Coming soon)
One Sided Derivatives
(Coming soon)
Derivatives and Continuity
(Coming soon)
Making Derivatives Exist
(Coming soon)
Existence of Higher Derivatives
(Coming soon)
Course description
Measure rates of change directly on graphs you can tap and zoom, watching a secant line settle into a tangent line as the interval shrinks. By the end of the course, you'll be able to find average rates of change from graphs and tables, work with negative rates through displacement and velocity, estimate the slope of a curve at a single point, write the equation of a tangent line, and read the limit definition of the derivative as something you built rather than memorized. You'll work out the derivatives of squares, lines, exponentials, and square roots from that definition, so the shortcut rules make sense when you meet them.
Topics covered
- Average Rate of Change
- Derivative Function
- Displacement
- Euler's Number
- Exponential Derivatives
- Limit Definition
- Linear Approximation
- Local Linearity
- Net Change
- Secant Lines
- Tangent Lines
- Velocity
Prerequisites and next steps
Before you get started, you should be comfortable reading graphs, working with function notation like f(x), and finding the slope of a straight line. You don't need any prior experience with calculus, limits, or derivatives to begin, and the course builds every derivative it computes from scratch rather than handing you rules to memorize. When you finish, you'll be ready to take on the shortcut rules for differentiation and the applications that follow.