POV-Ray : Newsgroups : povray.advanced-users : Taking and evaluating second partial derivatives : Re: Taking and evaluating second partial derivatives Server Time18 Sep 2024 18:11:18 EDT (-0400)
 Re: Taking and evaluating second partial derivatives
 From: Cousin Ricky Date: 23 Sep 2020 13:52:47 Message: <5f6b8b6f\$1@news.povray.org>
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On 2020-09-22 9:50 PM (-4), Bald Eagle wrote:
> [snip]
>
> But when I take first PARTIAL derivatives, this does NOT require the product
> rule, and I should get both
>
> Bdv = f'(v) * f(u) * c     _and_
>
> Bdu = f(v) * f'(u) * c
>
> and these are essentially tangents to the surface in the direction of u or v
>
>
>
> When I take second partial derivatives, I should get
>
> Bdvdv = f''(v) * f(u) * c,
> Bdvdu = f'(v) * f'(u) * c,
> Bdudv = f'(v) * f'(u) * c, and
> Bdudu = f(v) * f''(u) * c
>
> the f''s indicate concave up or down along u or v (the change of the slope of
> the tangent while traveling in that direction), but I'm a wee bit lost about the
> meaning of the mixed partials (which are equivalent, right?) Are they how the
> slope of the tangent changes as it gets "slid sideways" along the orthogonal
> direction?

Get back to me in the spring of 1983, and I'll explain it all.
```