§ 06 · Function evaluator
Type a curve. See its whole story.
Enter any function f(x) and the evaluator does the calculus for you: it plots the curve, differentiates it live for f′(x), and numerically integrates it for the running area ∫₀ˣf(t)dt. Use x, pi, e, and functions like sin, cos, exp, sqrt. Hover the graph to probe any point, or drag the marker at the bottom.
f(x)
f′(x)
∫₀ˣ f(t) dt
Hover to probe · drag the x marker to scrub · curves share one vertical scale
Probe x
–
f(x)
–
f′(x)
–
∫₀ˣ f(t) dt
–
The limit, zoomed in — a secant line collapsing onto the tangent at your probe point
| 2x, x sin(x) | implicit multiplication works |
| x^2, x^0.5 | powers (or use sqrt) |
| sin cos tan asin acos atan | trig (radians) |
| exp, ln, log, sqrt, abs | exponential, natural log, log₁₀, root, absolute value |
| pi, e | constants: 3.14159…, 2.71828… |
| Try: | x^2 * sin(3x) — where does its derivative cross zero? |
§ 07 · Multi-domain grapher
Wave, spectrum, and polar — the same f(x,t), three ways
This second grapher takes a function of x and time t and shows it three ways: the raw wave, its frequency spectrum (a live DFT), and a polar trace. Drag to pan, scroll to zoom, and try deriv(...) to differentiate any preset with respect to x.
Equation Input
KaTeX Formula Preview
$$f(x, t) = \sin(x - t)$$
Presets Library
Wave & Time Animation
Animation Speed
1.0x
Interactive Probe
Evaluate at x
Result f(x,t)
+0.0000
Viewport Axes Bounds
x Min
x Max
y Min
y Max
Time t = 0.00s
x: +0.0000 | y: +0.0000