OpenAha
00
All courses
Math · Advanced

Calculus: Derivatives

How fast is something changing right now? Shrink secant lines into tangents, discover the power rule, read the shape of a graph from its slope, discover why ee is special, master the product and chain rules, and use derivatives to find the best possible answer to real problems.

8 lessons~45 min0/8 complete
Start courseHelpful background: Functions & Graphs
1

The Idea of a Derivative

From average change to change at an instant.

  1. Speed at an InstantSecants shrink into tangents
  2. The DerivativeA slope for every point
2

Rules and Graphs

Shortcuts, and reading shapes.

  1. The Power RuleDerivatives without limits
  2. Reading ShapesWhat f′ says about f
3

Using Derivatives

Best answers, and the physics of motion.

  1. OptimizationFinding the best
  2. Calculus of MotionVelocity and acceleration as derivatives
4

More Rules

Sines, exponentials, products and chains.

  1. Sines and ExponentialsWhere e comes from
  2. Products and ChainsCombining rates of change

Courses that build on this

Ready for more? These courses use what you learn in Calculus: Derivatives.

Math · Advanced

Calculus: Integrals

Add up infinitely many tiny pieces: areas, volumes, distances and the Fundamental Theorem.

7 lessons4 chapters
Math · Advanced

Multivariable Calculus

Contour maps, partial derivatives, gradients, constrained optimisation and double integrals.

7 lessons3 chapters
Math · Advanced

Taylor Series

Approximating any smooth function with polynomials, and the physics hiding in the first few terms.

7 lessons3 chapters