Calculus is the mathematics of change. Instead of memorizing rules, drag a point, slide a value, and watch the ideas — slope, area, and the limit — unfold in front of you.
Open the derivative lab A growing set of hands-on explorers. No sign-up, nothing to install.Slide a point along a curve and watch the tangent's slope trace out the whole derivative f′(x).
Explore LiveAdd rectangles one by one — Riemann sums — and see them squeeze toward the exact integral.
Explore LiveWalk toward a point from both sides and see what value the function is really approaching.
Explore LiveAdd polynomial terms one at a time and watch them curl into the shape of the true curve.
Explore LiveSweep the upper limit and watch the running-area curve draw itself — its slope is exactly f(x).
Explore LiveHunt down every peak and valley, and let the second-derivative test name each one.
Explore LiveRead a differential equation as a field of tangents, then thread a solution curve through it.
Explore LiveChase a root down the tangent lines and watch the guess double its accuracy every step.
Explore LiveSpin a curve into a solid and stack disks until the sum becomes the exact volume, π∫f².
Explore LiveBetween any two points, a tangent must run parallel to the chord — find the guaranteed spot.
Explore LiveSlide a ladder at steady speed and watch the top race away — rates chained by the equation.
Explore LiveAdd up endless terms and watch the partial sums settle on a number — or wander off forever.
Explore LiveDrive both coordinates by a clock and trace loops, spirals, and flowers a function can't.
Explore LivePlay the rigorous-limit game: name a tolerance and find the window that keeps the curve inside.
Explore LiveTrap a region between two graphs and sum the gap — top minus bottom — into its area.
Explore LiveStraighten a curve with a chain of tiny segments until the total becomes ∫√(1+f′²).
Explore LiveFollow x through a two-stage pipeline and watch the rates at each stage multiply.
Explore LiveCrack a 0/0 limit by swapping the ratio of curves for the ratio of their tangent slopes.
Explore LiveRotate about the y-axis and build the solid from nested shells: 2π∫x·f(x)dx.
Explore LiveFan triangular wedges from the origin to sweep out a polar region: ½∫r²dθ.
Explore LiveFind the rectangle with the same area as the curve — and the point where f hits that height.
Explore LiveFind the tangent slope on a curve that isn't a function: dy/dx = −Fx/Fy.
Explore LivePush the boundary to infinity and see whether an endless region holds a finite area.
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