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.
What the Calculus Grapher: Derivative & Integral shows
Draw a function and see its derivative, or draw the derivative and see the function. Free, no signup, runs in your browser. Works on phones and computers. 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.
How to use the Calculus Grapher: Derivative & Integral
In the Calculus Grapher: Derivative & Integral, use the controls to change You draw, Start from, Tangent line. The simulation reacts instantly.
In the Calculus Grapher: Derivative & Integral, pick an option such as f(x) → see f'(x), f'(x) → see f(x), Parabola, Sine to switch modes or load an example.
In the Calculus Grapher: Derivative & Integral, press "Smooth curve" to start, reset or change what is happening.
Start with this experiment: Draw a hill and look at the slope graph. Drag any glowing handle, object or slider with your mouse or finger and the Calculus Grapher: Derivative & Integral responds in real time.
Change one setting at a time and watch which readout moves, then compare it with this idea: The derivative is the slope of the function.
Things to try
Draw a hill and look at the slope graph.
Switch to drawing f'(x).
Start from the sine preset.
The science behind it
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.
A worked example with real numbers
f'(x) = 2x, zero at x = 0 where f has its minimum -4.
Tips and common mistakes
Tips
- Find peaks where f' crosses zero.
- Draw f' first.
Common mistakes
- Mixing f and f'.
- Forgetting the constant of integration.
Where this is used
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. A good first experiment in the Calculus Grapher: Derivative & Integral: Draw a hill and look at the slope graph. The key relation to keep an eye on: f' is the slope of f; f is the area function of f'; fundamental theorem of calculus.
For teachers: project the Calculus Grapher: Derivative & Integral on the board, let students predict the result, then run it together and test this: Switch to drawing f'(x). 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. The Calculus Grapher: Derivative & Integral is free, needs no signup or download and runs in your web browser. It is part of the Math group of AZRS simulations.
Does the Calculus Grapher: Derivative & Integral work on a phone or tablet?
Yes. The Calculus Grapher: Derivative & Integral takes touch input as well as mouse input, so you can use its 3 adjustable settings with a finger. A larger screen makes the controls and graphs easier to read.
