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Compute the spline representation of the derivative of a given spline
.. legacy:: function
Specifically, we recommend constructing a `BSpline` object and using its
``derivative`` method.
Parameters
----------
tck : BSpline instance or tuple
BSpline instance or a tuple (t,c,k) containing the vector of knots,
the B-spline coefficients, and the degree of the spline whose
derivative to compute
n : int, optional
Order of derivative to evaluate. Default: 1
Returns
-------
`BSpline` instance or tuple
Spline of order k2=k-n representing the derivative
of the input spline.
A tuple is returned if the input argument `tck` is a tuple, otherwise
a BSpline object is constructed and returned.
See Also
--------
splantider, splev, spalde
BSpline
Notes
-----
.. versionadded:: 0.13.0
Examples
--------
This can be used for finding maxima of a curve:
>>> from scipy.interpolate import splrep, splder, sproot
>>> import numpy as np
>>> x = np.linspace(0, 10, 70)
>>> y = np.sin(x)
>>> spl = splrep(x, y, k=4)
Now, differentiate the spline and find the zeros of the
derivative. (NB: `sproot` only works for order 3 splines, so we
fit an order 4 spline):
>>> dspl = splder(spl)
>>> sproot(dspl) / np.pi
array([ 0.50000001, 1.5 , 2.49999998])
This agrees well with roots :math:`\pi/2 + n\pi` of
:math:`\cos(x) = \sin'(x)`.
A comparison between `splev`, `splder` and `spalde` to compute the derivatives of a
B-spline can be found in the `spalde` examples section.
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