# How do CAS evaluate derivatives

 Sci Advisor P: 833 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 $\sin(x^2)+3$ would be Plus[3,Sin[Power[x,2]]] 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 D[Sin[Power[x,2]]] It allies its chain rule and is programmed so that D[Sin] = Cos: Multiply[Cos[Power[x,2]],D[Power[x,2]]] And we know that the derivative of Power[x,2] as Multiply[2,x]