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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §13.5 The Chain Rule, #48 · Multivariable Calculus · Partial derivatives

Prove that …, by computing the … derivative at

A function has constant returns to scale if $f (c x, cy) = c f (x, y)$ . When $x$ and $y$ are doubled so are $f = x^{2} + y^{2}$ and $f = x y$ . In economics , input/output is constant. In mathematics $f$ is homogeneous of degree one.

Prove that $x \partial f / \partial x + y \partial f / \partial y = f (x, y)$ , by computing the $c$ derivative at $c = 1$ . Test this equation on the two examples and find a third example.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §13.5 The Chain Rule, #48

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