I am having difficulty understanding this differentiation question

Question

SO I have this question:

I think the question is asking me to do a a partial differentiation to find dx/ds, dy/ds, dz/ds which I have found in my solution, but I am not confident with the approach I took to solve this question. My solution for those are as following:

Can someone please tell me if I am on the right path and secondly the question asks to find df/ds which I am not sure how to find.

cvanaret · Answer

As Kevin said, apply the chain rule to $phi(s) = f(x(s), y(s), z(s))$:
$frac{d phi}{ds}(x(s), y(s), z(s)) = frac{partial f}{partial x}(x(s), y(s), z(s)) frac{dx}{ds}(s) + ldots$

I am having difficulty understanding this differentiation question

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