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I am reading Hugo D. Junghenn's book: "A Course in Real Analysis" ...

I am currently focused on Chapter 9: "Differentiation on \mathbb{R}^n"

I need some help with an aspect of Definition 9.1.3 ...

Definition 9.1.3 and the relevant accompanying text read as follows:

At the top of the above text, in Definition 9.1.3 we read the following text:

" ... ... there exists a vector ##f'(a)## in ##\mathbb{R}^n## ... ... "My question is as follows:

How (arguing from the definition of derivative) do we indicate\demonstrate\prove that ##f'(a) \in \mathbb{R}^n## ... ...?Hope someone can help ... ...

Peter

I am currently focused on Chapter 9: "Differentiation on \mathbb{R}^n"

I need some help with an aspect of Definition 9.1.3 ...

Definition 9.1.3 and the relevant accompanying text read as follows:

At the top of the above text, in Definition 9.1.3 we read the following text:

" ... ... there exists a vector ##f'(a)## in ##\mathbb{R}^n## ... ... "My question is as follows:

How (arguing from the definition of derivative) do we indicate\demonstrate\prove that ##f'(a) \in \mathbb{R}^n## ... ...?Hope someone can help ... ...

Peter