# Differential Geometry, easy question, weird hint making me doubt myself

## Homework Equations

From my notes: $$(\psi_{*}v)_{k}(x)=\sum_{i=1}^{n}v_{i}(x)\frac{{{{{\partial}}}}{\psi_{k}(x)}}{{x_{i}}}$$

## The Attempt at a Solution

Okay so i) is fine (ignoring the typo in the question) but I'm a bit confused about ii)

I don't see any need to bore people with the details but I simply computed $(\psi_{*}v)(x)$ and then did the same for $w$ from the definition and got exactly what I wanted. My question is, is there something I've missed i.e. is there a good reason for that hint to be there? My problem is that if it's as easy as it looks, then I don't see why he would feel the need to give us a hint and then I don't see how using the hint would help get me the wanted answer.

Bear in mind this is assessed to vagueness is wanted.

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