First Principles of Differentiation

Explore the definition of derivative through interactive visualization.

First Principles

Exploring derivatives as the limit of secant slopes.

Variables

Position (x)1.00
Offset (h)1.50

Slope Calculation

Δy = f(x+h) - f(x)0.5070
Slope (m)0.3380

Analysis

SECANT LINE

Guide

  • Drag the red point () toward to see .
  • Watch the derivative graph below plot the instantaneous slope.

Function & Secant / Tangent Line

y = f(x)
h = 1.50Δyxx+h

The First Derivative Graph

f'(x) = cos(x) + 0.5
y = f'(x)
m = 0.34