Calculus Circus

AP Calculus practice

Derivative Rules and Differentiation Practice

Learn and practice derivatives the way AP Calculus teaches them: from rate of change through the power rule, product rule, and trigonometric derivatives. Calculus Circus has 21 differentiation skills across 6 topics. 13 skills are free, including Power Rule subskills. Start a free skill now, then sign in when you want Calculus Circus to remember your progress.

Start practicing free Sign in to save progress

Sign in to keep completions, track your progress, and make your learning visible to your teacher. Derivative Concepts, Power Rule, Product Rule, and Trigonometric Derivatives are free. Natural log, natural exponential, and curve sketching require full access — a flat annual fee with no automatic renewal.

What you will practice

A derivative describes how a function is changing at a point. AP Calculus asks students to read that idea from tables, graphs, and expressions, then compute derivatives and use them to describe the graphs of functions.

If f(x) = x³, then f′(x) = 3x². The power rule turns an exponent into a coefficient and reduces the power by one.

The six differentiation topics

  1. Derivative Concepts

    5 free skills

    Rate of change and average rate of change from a table, a graph, a function expression, and a mixed set.

    Practice derivative concepts

  2. Power Rule

    5 free skills, plus subskills

    Integer, negative, fractional, and negative fractional exponents, then a mixed power rule set.

    Practice the power rule

  3. Product Rule

    1 free skill

    Differentiate a product of two functions.

    Practice the product rule

  4. Trigonometric Derivatives

    2 free skills

    Derivatives of sine, cosine, and tangent, then the chain rule on trigonometric functions.

    Practice trigonometric derivatives

  5. Derivatives of the Natural Log and Natural Exponential

    5 skills · full access

    Natural exponential and natural log derivatives, including more complex forms and a mixed set.

    See natural log and exponential derivatives

  6. Curve Sketching

    3 skills · full access

    Use the first and second derivative to describe increasing and decreasing behavior, concavity, and the shape of a graph.

    See curve sketching

How practice works

  • Short problem sets with instant feedback.
  • Skills arranged in a pathway.
  • Derivative Concepts, Power Rule and its subskills, Product Rule, and Trigonometric Derivatives are free. Sign in to save your progress or join a class created by your teacher.
  • Derivatives of the natural log and natural exponential, and curve sketching, require full access — a flat annual fee with no automatic renewal. Teachers can see how Calculus Circus works on the About page.

Derivatives practice FAQ

What derivative skills can I practice here?

There are 21 skills across the six topics above: derivative concepts, the power rule, the product rule, trigonometric derivatives, natural log and natural exponential derivatives, and curve sketching.

Which derivative skills are free?

Derivative Concepts (5), Power Rule (5, plus subskills), Product Rule (1), and Trigonometric Derivatives (2) are free. Natural log and natural exponential derivatives (5) and curve sketching (3) require full access.

Do I need an account to start?

No. You can begin the free derivative skills without an account. Sign in when you want Calculus Circus to keep your completions.

Why should I sign in?

Signing in saves progress so you can return to the next skill and, if you join a class, so a teacher can see where you are practicing.

What comes after derivatives?

After differentiation, students typically move into integration.

Ready to try a derivative skill?

Open the differentiation pathway and start with derivative concepts, or jump to the power rule. Sign in if you want Calculus Circus to save your place.

Start practicing free Sign in to save progress