On Mon, Aug 25, 2008 at 8:58 PM, Tim Lahey <[EMAIL PROTECTED]> wrote: > On Aug 25, 2008, at 11:45 PM, William Stein wrote: > >> >> The chain rule from calculus says that if f(x) = g(h(x)) then >> >> df/dx = (dg/dh) * (dh/dx). >> >> Dividing both sides by dh/dx we see that >> >> dg / dh = (df /dx) / (dh/dx). >> >> I thus suspect that when you say "differentiate g(h(x)) >> with respect to h" you might mean to compute dg/dh, >> as defined by the chain rule above. >> > > Yes, but that's a) a horribly inefficient way of doing > that and b) in my case, impossible. I don't know h(x) > because I'm trying to solve for it. It's the whole point > of the system of PDEs. But, dg/dh is easily computable if > you have g which I have. > > The point is that differentiation with respect to a function > or a variable should be equivalent.
I only meant it as a definition to help clarify the discussion, not as an algorithm. Many thanks for your additional clarification. William --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
