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DerivativeOver(AngouriMath.Entity.Variable)

Method (no overloads)

Summary

The derivative over variable, unsimplified: zero for a node that is
a constant in it, and the node's own rule, InnerDifferentiate(AngouriMath.Entity.Variable),
for any other. Every rule asks this of its parts rather than asking their rules.

Remarks

A rule writes the chain rule, and its outer factor can have no value where the node
has one: sqrt(c) gave 1/2 c^(-1/2) * 0, and arcsin(c) a factor
with no value at c = 1. Zero times a factor keeps the condition the factor is
defined under, so sqrt(c) x differentiated to sqrt(c) provided not c = 0,
with no value at c = 0, where the derivative is sqrt(0) = 0; an
antiderivative carrying sqrt(D) had no value anywhere at a discriminant
D = 0. Nothing varies with the variable here, so the answer is zero with no
condition, as it already was for a node with no rule of its own, the modulus and the
sign. That holds where the constant has no value too, ln(c - c): a derivative is
claimed only where the expression has a value.
Not where a zero loses what the node says besides a value. A set or a matrix is
differentiated elementwise, { 1, 2 } to { 0 }. A provided and a
piecewise keep their own conditions, which their rules write onto the derivative. A
written NaN stays NaN, as Number's rule keeps it. Their rules reach the
constants inside them through this method.

AngouriMath

Table of contents

AngouriMath

DerivativeOver​(AngouriMath.​Entity.​Variable)

DerivativeOver(AngouriMath.Entity.Variable)