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Calculus explorer: gradients and areas from first principles

Drag points directly on the graph or use the sliders to see how a chord gradient approaches the derivative and how rectangle sums approach the definite integral.

Tip: drag point P or point Q directly on the curve, or use the sliders and step presets.

Differentiation from first principles

Base point x (point P) x = 1.00

Step size h (horizontal distance to Q) h = 1.500

Snap h:

Differentiation from first principles

Riemann rectangles and definite integral