On Sep 18, 6:43 pm, kcrisman <[email protected]> wrote: > Actually, the subject of your email now makes a little more sense. > But I don't think that one can define an inverse function quite this > easily! That would indeed be *very* obscure notation! I don't know > if we can define a symbolic inverse of this kind yet, or whether that > would even be easy - much less to differentiate it. Anyone?
Finding an expression for the derivative of an inverse is part of most first calculus courses: Suppose that f : R -> R is a differentiable function and that y=f(x). Suppose that g : R -> R is an inverse to f, i.e., x=g(y). Find an expression for g'(y) in terms of f'(x). [HINT: use the chain rule on f(g(y) or g(f(x))] One usually continues with stating the inverse function theorem to conclude that if this computation doesn't rule out the existence of a differentiable inverse, then the inverse exists locally, an expression for which you can now find by integration [so, probably rather hard to do in general on a symbolic level] -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
