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How do CAS evaluate derivatives

  1. Feb 18, 2012 #1
    How do CAS systems and programmable calculators evaluate the derivative of a function?
    Do they use matrix representation of linear transformations?
  2. jcsd
  3. Feb 19, 2012 #2

    Stephen Tashi

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    I don't know the answer, but you should specify whether you are asking how they evaluate derivatives numerically or how they evaluate them symbollically. Is the result of the evaluation a formula? Or a graph? Or a numerical table?
  4. Feb 19, 2012 #3
    Sorry for being vague but I meant symbolically.
  5. Feb 19, 2012 #4
    I suspect that they convert whatever expression you want to differentiate into taylor series, differentiate (in the obvious way), then match the result to a taylor series that represents an elementary function and substitute back. Maybe not, but I can't imagine how else it would be done.
  6. Feb 19, 2012 #5


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    From what I heard CAS stores the information as a directed graph. In Mathematica you can use the FullForm command to see it directly for example
    would be
    It then has rules for how to manipulate these objects. So the derivative operator D (I'm assuming wrt x) interacts with Plus via the rule
    D[Plus[f,g]] = Plus[D[f],D[g]]
    Mathematica knows that 3 is constant and so D[3]=0. It then reduces Plus[0,?] to just ?.
    So we now have
    It allies its chain rule and is programmed so that D[Sin] = Cos:
    And we know that the derivative of Power[x,2] as Multiply[2,x]
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