Calculus Grapher: Derivative & Integral
Draw a function and see its derivative, or draw the derivative and see the function.
Draw the top graph by dragging across it. The derivative (slope) graph below is drawn automatically. Or switch mode and draw the derivative to build the function.
About the Calculus Grapher: Derivative & Integral
Free calculus grapher: derivative & integral. Draw a function and see its derivative, or draw the derivative and see the function. Drag, change the sliders and see the result live. No sign-up, works on phone and computer. Built for math, the calculus grapher: derivative & integral runs instantly in your browser: change a setting or drag an object and the result updates at once, so you learn by trying things out rather than only reading about them.
Draw a function and see its derivative, or draw the derivative and see the function. Use it to explore math ideas at your own pace, then check what you found against the key ideas further down this page.
How to use the Calculus Grapher: Derivative & Integral
- Use the controls to change You draw, Start from, Tangent line. The simulation reacts instantly.
- Pick an option such as f(x) → see f'(x), f'(x) → see f(x), Parabola, Sine to switch modes or load an example.
- Where you see a glowing handle, object, weight or atom, drag it with your mouse or finger. Everything responds in real time.
- Watch the readouts and graphs update as you experiment, and compare what you see with the key ideas below.
Things to try
- Draw a hill and look at the slope graph.
- Switch to drawing f'(x).
- Start from the sine preset.
Key ideas you can learn
- The derivative is the slope of the function.
- Where the function has a peak, the derivative is zero.
- The integral is the area under the derivative.
- Derivative and integral undo each other.
Where this is used in the real world
Physics, economics and engineering use derivatives for rates and integrals for totals.
Who is this simulation for?
Algebra, geometry, trigonometry and calculus students, teachers preparing demonstrations, and self-learners who want to see the maths move.
For teachers: project it on the board, let students predict what will happen, then run it together. For students: change one thing at a time and write down what changes.
Frequently asked questions
What does the derivative tell you?
How fast the function is changing at each point: its slope.
How are derivatives and integrals related?
They are inverse operations (the fundamental theorem of calculus).
Is the Calculus Grapher: Derivative & Integral free to use?
Yes. It is completely free, with no signup, no download and no ads inside the simulation. It runs in your web browser.
Does the Calculus Grapher: Derivative & Integral work on a phone or tablet?
Yes. It uses touch as well as the mouse, so you can drag objects with your finger. A larger screen makes the controls easier to see.