Derivative Visualizer
Drag a point along a curve and see the tangent line and the derivative graph appear.
Drag the orange point along the curve. The tangent line and the derivative graph follow it.
About the Derivative Visualizer
Free derivative simulator. Drag a point along a function, see the tangent line, its slope, and the derivative curve draw itself. Includes polynomials, sine, exponential and more. Built for math, the derivative visualizer 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.
Drag a point along a curve and see the tangent line and the derivative graph appear. 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 Derivative Visualizer
- Use the controls to change Or type your own f(x), Secant gap h. The simulation reacts instantly.
- Pick an option such as Tangent, Secant, Derivative graph 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
- Drag the point to the top of a hill. What is the slope?
- Pick sin(x) and compare with its derivative curve.
- Shrink the secant gap h and watch the secant become the tangent.
- Find where x² has slope 4.
Key ideas you can learn
- The derivative at a point is the slope of the tangent line there.
- Where the function has a peak or dip, the derivative is zero.
- Increasing functions have a positive derivative, decreasing ones negative.
Where this is used in the real world
Derivatives measure rates of change in physics, economics, biology and machine learning, from speed to growth rates to optimisation.
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 is the derivative geometrically?
The slope of the tangent line to the curve at a point, which is the instantaneous rate of change.
Why is the derivative zero at a maximum?
At the very top the curve is momentarily flat, so its tangent is horizontal and the slope is zero.
Is the Derivative Visualizer 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 Derivative Visualizer 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.