Mathematical Methods · differentiation rules · manipulative

The chain rule multiplies two rates

y is a function of u, and u is a function of x. The two graphs measure those two rates — multiply them to get how fast y changes with x.

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×
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=
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du/dx tangent dy/du tangent shared u

Inner: u = g(x)

Outer: y = f(u)

Drag across the inner graph to move x — the violet line carries u down to the outer graph

Point x

0.5

Working