Calculus Grapher: free math simulation
Type any function and see its derivative, integral and a draggable tangent line.
▶ Open the simulationFree, no sign-up. Works on phones, tablets and laptops.
The science
The derivative of a function is the slope of its graph at each point, and the integral is the area under the graph. Dragging a tangent line along a curve shows the derivative changing live.
f′(x) = lim (f(x+h) − f(x)) / h
Things to try
- Type x^2 and check the derivative is a straight line.
- Find where the derivative of sin(x) is zero.
- Watch the integral of a constant grow as a straight line.
Topics covered
derivative integral tangent area function graph
How to use it
Open the simulation, then change the experiment live with the sliders, checkboxes and buttons in the side panel. Drag objects on screen where it makes sense, and use Pause, Step, Speed and Reset in the bottom bar to study every moment.
Frequently asked questions
What does the Calculus Grapher simulation show?
The derivative of a function is the slope of its graph at each point, and the integral is the area under the graph. Dragging a tangent line along a curve shows the derivative changing live.
What is the key equation?
f′(x) = lim (f(x+h) − f(x)) / h
Is the Calculus Grapher simulation free?
Yes. It runs free in any web browser on phones, tablets and laptops, with no sign-up or download.
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