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Action:
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Creates a
law object that is the derivative of the given law with respect to the given variable.
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Filename:
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kern/kern_scm/law_scm.cxx
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Syntax:
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(law:derivative law [with-respect-to])
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Arg Types:
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law
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law | string | real | position |
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par-pos | gvector
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with-respect-to
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law | string
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Returns:
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law
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Description:
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The
law:derivative returns the exact derivative of the given
law function.
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law specifies a law.
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with-respect-to is an optional argument specifying an identity law, such as x, y, z, or a#, etc. If
with-respect-to is provided, then the derivative is performed with respect to this argument; else the derivative is assumed to be with respect to
x or
a1.
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Example:
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; law:derivative
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; Define a law to use.
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(define law1 (law "x^2"))
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;; law1
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; To get exact results, take the exact derivative.
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; Create the derivative of that law.
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(define d-law (law:derivative law1))
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;; d-law
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; Evaluate the derivative.
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(law:eval d-law 3)
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;; 6
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; Evaluate the second derivative.
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(law:eval (law:derivative d-law) 3)
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;; 2
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; Find the numerical derivative at 3.
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(law:nderivative law1 3 "x" 1)
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;; 5.9999999999838
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; Find the second numerical derivative at 3.
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(law:nderivative law1 3 "x" 2)
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;; 1.9999997294066
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