Derivative Explorer

Derivative Explorer — See the Tangent Line and Slope f′(x)

The derivative is just the slope of the tangent line, and this explorer makes that idea move. Slide a point along a curve and the tangent pivots with it; its slope is f′(x) — positive where the curve rises, negative where it falls, and zero at the turning points. Switch functions and overlay the whole derivative curve to see the connection at a glance.

What you can do in this simulation

• Slide a point along the curve and watch the tangent line pivot
• Read f(x) and the slope f′(x) at the point in real time
• See the slope go positive, negative, and zero at peaks and valleys
• Overlay the full derivative curve and check where it crosses zero
• Switch between a cubic, a parabola, and a sine wave

Concepts covered

derivative · tangent line · slope · rate of change · turning points · increasing and decreasing · calculus

Free to use in your browser — no signup required. Found a bug or have an idea to make it better? Tell us.