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Differentiate function

`fprime = fnder(f,dorder) fnder(f) `

`fprime = fnder(f,dorder) `
is the description of the `dorder`th derivative
of the function whose description is contained in `f`.
The default value of `dorder` is 1. For negative `dorder`,
the particular |`dorder`|th indefinite integral is
returned that vanishes |`dorder`|-fold at the left
endpoint of the basic
interval.

The output is of the same form as the input, i.e., they are
both ppforms or both B-forms or both stforms. `fnder` does
not work for rational splines; for them, use `fntlr` instead. `fnder` works
for stforms only in a limited way: if the type is `tp00`,
then `dorder` can be `[1,0]` or `[0,1]`.

`fnder(f) ` is the same
as `fnder(f,1)`.

If the function in `f` is multivariate, say *m*-variate,
then `dorder` must be given, and must be of length *m*.

If `f` is in ppform, or in B-form with its
last knot of sufficiently high multiplicity, then, up to rounding
errors, `f` and `fnder(fnint(f))` are
the same.

If `f` is in ppform and `fa` is
the value of the function in `f` at the left end
of its basic interval, then, up to rounding errors, `f` and `fnint(fnder(f),fa)` are
the same, unless the function described by `f` has
jump discontinuities.

If `f` contains the B-form of *f*,
and *t*_{1} is its leftmost knot,
then, up to rounding errors, `fnint(fnder(f))` contains
the B-form of *f* – *f*(*t*_{1}).
However, its leftmost knot will have lost one multiplicity (if it
had multiplicity > 1 to begin with). Also, its rightmost knot will
have full multiplicity even if the rightmost knot for the B-form of *f* in `f` doesn't.

Here is an illustration of this last fact. The spline in `sp
= spmak([0 0 1], 1)` is, on its basic interval [`0`..`1`],
the straight line that is 1 at 0 and 0 at 1. Now integrate its derivative: `spdi
= fnint(fnder(sp))`. As you can check, the spline in `spdi` has
the same basic interval, but, on that interval, it agrees with the
straight line that is 0 at 0 and –1 at 1.

See the examples "Intro to B-form" and "Intro to ppform" for examples.

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