Derivative of Composite Function/3 Functions
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Theorem
Let $f, g, h$ be continuous real functions such that:
\(\ds y\) | \(=\) | \(\ds \map f u\) | ||||||||||||
\(\ds u\) | \(=\) | \(\ds \map g v\) | ||||||||||||
\(\ds h\) | \(=\) | \(\ds \map h x\) |
Then:
- $\dfrac {\d y} {\d x} = \dfrac {\d y} {\d u} \cdot \dfrac {\d u} {\d v} \cdot \dfrac {\d v} {\d x}$
Proof
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Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): chain rule (for differentiation)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): chain rule (for differentiation)