Re: [Mathlib-develop] Re: Symbolic calculations

[mark <msp...@ya...>]

On Wednesday 12 Feb 2003 6:55 pm, Stefan Mueller wrote:
> >>Hi Mark and Stefan!
> >>
> >>1) Why don't we put it on a new class on Functions/Calculus package? =
I
> >> have free access to some "numerical methods" books at the university=
, so
> >> if you need it I'll pass you some hints.
> >
> > What I meant was how to handle cases like derivative( sin(x), x) =3D>
> > cos(x) or even derivative( UserFunction(x), x) =3D> OtherFunction(x)
> >
> > My idea was that the implementation of sin and UserFunction would con=
tain
> > a method called derivative which would return the correct value.
>
> I aggree to add the two methods to the individual functions.
> But what about complex integration/derivative rules, like the chain
> rule?
> e.g.: d/dx of sin(cos(x))
>

IIRC d/dx f(u) =3D d/dx u * d/du f(u)=20

so d/dx sin(cos(x)) =3D -sin(x) * cos(cos(x))

So differentiating chained functions shouldn't be too hard.

Though we should probably limit derivatives to functions that take 1=20
parameter.

Best Regards

Mark