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. Cheers, Tim.
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