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 at a Point
The Limit Definition of Derivative
Interpreting Limits as Derivatives
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 f’(x)
(Coming soon)
Derivatives of Piecewise Functions
(Coming soon)
Increasing and Decreasing
(Coming soon)
Identifying the Derivative Graph
(Coming soon)
Growing Squares
(Coming soon)
The Power Rule
(Coming soon)
The Sum Rule
(Coming soon)
The Constant Multiple Rule
(Coming soon)
Differentiating Polynomials
(Coming soon)
The Derivative of Sine
(Coming soon)
The Derivative of Cosine
(Coming soon)
Differentiating the Exponential Function
(Coming soon)
Differentiating the Natural Logarithm
(Coming soon)
Growing Rectangles
(Coming soon)
The Product Rule
(Coming soon)
Using the Product Rule
(Coming soon)
Power Rule and Product Rule
(Coming soon)
The Power Rule for any exponent
(Coming soon)
Compression and Dilation
(Coming soon)
The Exponential Derivative, Revisited
(Coming soon)
Compositions of Functions
(Coming soon)
The Chain Rule
(Coming soon)
Differentiating any Function
(Coming soon)
Derivatives of Inverse Functions
(Coming soon)
Implicit Differentiation
(Coming soon)
Growing Circles
(Coming soon)
Changing Triangles
(Coming soon)
Filling Tanks
(Coming soon)
The Ideal Gas Law
(Coming soon)
Concavity
(Coming soon)
Points of Inflection
(Coming soon)
Critical Points
(Coming soon)
The 2nd Derivative Test
(Coming soon)
Curve Sketching
(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.