AngouriMath

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WithTheDerivativesTaken​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable,​AngouriMath.​Entity,​AngouriMath.​Core.​ApproachFrom)

 Method (no overloads)

Summary

expr with each derivative node that differentiates in closed form replaced by what
it differentiates to.

Remarks

A derivative is a function of the point it is taken at, and its limit is that function's limit, not the
derivative of the limit. Read as a node, the point was put in before differentiating: derivative(ln(x y), y)
at 0 became the derivative of the constant ln(0) and was answered 0, where it is 1 / y; and
derivative(sqrt(x), x) at 0 put 0 in for the variable too, and came back derivative(0, 0). A derivative
that does not close is left as it is.
What it differentiates to is inner-simplified. Differentiating states where the derivative exists, as
1 / x provided not x = 0 for ln(x), and a limit is taken on the way in and not at the point: the condition is
dropped where it holds on each side approached, and kept, which the limit declines, where it does not.
In a method of its own, so that the closure is not allocated for every limit.

























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