Candid Tools

Derivative Explorer

Derivative Explorer links secant slopes, tangents and derivative graphs for preset functions, with draggable points and local browser calculations.

f(x) = x²
f′(x) = 2x
1
0.8

Secant slope

2.8

Tangent slope

2

Slope difference

0.8
Two points become one tangentFunctionSecantTangent
-3-3-1.50.2503.51.56.75310xf(x)

Second point: x + h = 1.8. It can lie beyond the displayed window.

The derivative records every tangent slopeDerivativeTraced to x
-3-7.44-1.5-3.72001.53.7237.44xf′(x)

At a glance

Accepts
Five function presets, a point, spacing and approach direction
Outputs
Linked function and derivative graphs with exact preset derivatives and secant slopes
Where it runs
Entirely in your browser, on your device
What leaves your device
No calculation inputs are uploaded; standard site usage analytics still apply
Limits
Preset functions only; absolute-value derivative is undefined at zero
Account
Not required - there is no sign-up
Price
Free, with no watermark and no usage cap
Made by
Visrut
Last updated
14 October 2026

What to notice

The secant measures [f(x + h) − f(x)] / h between two points. The tangent uses the derivative at one point. Shrink |h| and compare both slopes; approach from either side.

At the corner of |x|, the left slope is −1 and the right slope is +1. They do not agree, so there is no derivative at zero. The derivative graph has a gap there.

Reference: defining the derivative

Frequently asked questions

Are these symbolic calculators?

These tools teach through supported function presets, exact derivatives and antiderivatives where supplied, and labelled numerical approximations. They do not evaluate arbitrary expressions.

Do calculations leave my device?

All graphs and calculations run locally in your browser. No account or external calculation service is required.