# I Computing the Directional Derivative ...

#### Math Amateur

Gold Member
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 $v_p[f]$ where $f$ is given as $f(x) = x$ ... .... BUT ... $v$ and $p$ are given in $\mathbb{R}^3$ ... so doesn't $f$ need to be defined on $\mathbb{R}^3$ ... say something like $f(x,y, z) = x$ or similar ...

Help will be appreciated ...

Peter

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#### pasmith

Homework Helper
I agree; none of the examples given in 2.4(a) make sense as functions from $\mathbb{R}^3$ to $\mathbb{R}$.

Are there any hints or solutions in the text which shed light on what the author intended to say here?

"Computing the Directional Derivative ..."

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