Tracy Harms wrote: > In that posting the chain > rule is given by the following expression: > > deriv (f . g) x = deriv f (g x) . deriv g x > > I'm confused by the use of composition on the right-hand side, as I > expect it to involve two functions. I can't see a composition of two > functions here; in J terms, I see nouns where I expect verbs. > Guidance in correcting my misinterpretation is welcome.
The problem is that if f is a function of one variable, f'(17) is usually interpreted as a number. To generalize it, you have to think about it as a linear map. When we write f'(17)=4, we really mean f'(17) is the linear map L:R->R such that L(x)=4x. With this interpretation, composition in the 1-dimensional case is the same as multiplication. More generally, if f:R^n -> R^m, its derivative at a point is a linear map from R^n->R^m, and can be interpreted as an m x n matrix. Best wishes, John ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
