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I am reading Jon Pierre Fortney's book: A Visual Introduction to Differential Forms and Calculus on Manifolds ... and am currently focused on Chapter 2: An Introduction to Differential Forms ...

I need help with Question 2.4 (a) (i) concerned with computing a directional derivative ...

Question 2.4, including the preceding definition of a directional derivative, reads as follows:

My question/problem is as follows:

In question 2.4 (a) (i) we are asked to find \(\displaystyle v_p[f]\) where \(\displaystyle f\) is given as \(\displaystyle f(x) = x\) ... .... BUT ... \(\displaystyle v\) and \(\displaystyle p\) are given in \(\displaystyle \mathbb{R}^3\) ... so doesn't \(\displaystyle f\) need to be defined on \(\displaystyle \mathbb{R}^3\) ... say something like \(\displaystyle f(x,y, z) = x\) or similar ...

Help will be appreciated ...

Peter

I need help with Question 2.4 (a) (i) concerned with computing a directional derivative ...

Question 2.4, including the preceding definition of a directional derivative, reads as follows:

My question/problem is as follows:

In question 2.4 (a) (i) we are asked to find \(\displaystyle v_p[f]\) where \(\displaystyle f\) is given as \(\displaystyle f(x) = x\) ... .... BUT ... \(\displaystyle v\) and \(\displaystyle p\) are given in \(\displaystyle \mathbb{R}^3\) ... so doesn't \(\displaystyle f\) need to be defined on \(\displaystyle \mathbb{R}^3\) ... say something like \(\displaystyle f(x,y, z) = x\) or similar ...

Help will be appreciated ...

Peter

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