Given a surface defined implicitly by a function like $f(x,y,z) = c$, I'm trying to show that $\frac{dx}{dy}\frac{dy}{dz}\frac{dz}{dx} = -1 $ for derivatives taken along the surface. I have no clue where to start on this, it seems like by the chain rule it ought to be 1.
Asked
Active
Viewed 18 times
2
-
Why do you think such a relation should be valid ? What is your approach towards obtaining the relationship? Have you considered a simple surface, such as $x + y + z = c$? Have you considered the two-dimensional version, with a function $f(x,y) = c$? – M. Wind May 18 '15 at 20:55
-
I really don't know, but I was working through some of the cambridge past tripos papers http://maths.cam.ac.uk/undergrad/pastpapers/2011/ia/PaperIA_2.pdf <- that is a link to the question – Peter Booth May 18 '15 at 21:07