Live measurements
- Point x-coordinate
- 1.00
- Point y-coordinate
- -1.00
- Tangent gradient f′(x)
- 2.00
- Secant gradient
- 3.00
- Gradient difference
- 1.00
MathematicsA-Level9 minBeta
Calculus Tangent & Derivative Explorer
Move a point along four reviewed curves, shrink a secant interval and see average gradient converge on the tangent gradient and derivative.
Model presets
Reviewed starting statesCurriculum map
- AQA A-Level Mathematics
Differentiation → Gradient functions, tangents and rates of change - Edexcel A-Level Mathematics
Differentiation → First principles and tangents to curves
Model boundaries
- Gradients use exact analytic derivatives for the four reviewed functions.
- The secant uses a positive forward interval Δx and illustrates a right-hand limit only.
- The graph view is automatically scaled and is intended for conceptual comparison rather than numerical measurement from pixels.
StudyVector-authored calculus model using standard analytic derivatives and difference quotients; mapped to the reviewed A-Level topics shown below.
Accessible text description
A Cartesian graph plots one reviewed function. A primary point at x and a second point at x plus delta x define a cyan secant and a labelled rise-over-run triangle. An orange tangent passes through the primary point. Formula cards show the function, derivative, secant gradient, tangent gradient and their difference. Native buttons move x and change delta x without requiring pointer precision.