Derivative of the composite function

The heart of the chapter: how to differentiate a composition of functions, such as $\sin(x^2)$, $e^{\sqrt{x}}$, $\arctan(1/x)$. The circle diagram method represents the composition as a chain of links, calculates the derivative of each link with geometric symbols as placeholders, and then multiplies and substitutes. It is the visual version of Leibniz’s chain rule.

• The circle diagram method
• x)
• Circle diagram — three links
• Composition with an inner product rule
• Catalogue of composite derivatives
• The chain rule in Leibniz notation