Differential Calculus and Its Applications by Unknown

Author:Unknown
Language: eng
Format: epub
ISBN: 0000000000000
Published: 2021-06-30T14:54:37+00:00

f(p)(x) = Dpfx(1, …, 1),

and

It follows again from Proposition 2.9.3 that

The case when F1 = F2 = · · · = Fn = R is particularly important.

Proposition 2.9.4

Let A be an open subset of R and suppose f =(f1, …, fn) : A Rn. Then f is p times differentiable at x ∈ A if and only if each component function is p times differentiable at x.

The derivatives of f and the components of f are related by

or, in classical derivative notation, by

Example. Let f : R R³ be defined by

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