Chain rule (3D)

About this app

Two composed functions in 3D: x → u = g(x) → y = f(u). Slope triangles at P and Q share the common Δu — the teal pulsing "hinge" stroke makes visible why the derivatives multiply. Four combinations to choose from.

Subject: Analysis (one-dimensional)

More from Analysis (one-dimensional)

• Derivative as a sequence of secants
• Bounded growth
• Exponential growth and decay
• Optimisation: the largest rectangle
• Area between curves
• Area function is an antiderivative
• Sequential continuity
• Rational functions and asymptotes

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