Register to reply

How do CAS evaluate derivatives

Share this thread:
matqkks
#1
Feb18-12, 01:25 PM
P: 153
How do CAS systems and programmable calculators evaluate the derivative of a function?
Do they use matrix representation of linear transformations?
Phys.Org News Partner Science news on Phys.org
Scientists discover RNA modifications in some unexpected places
Scientists discover tropical tree microbiome in Panama
'Squid skin' metamaterials project yields vivid color display
Stephen Tashi
#2
Feb19-12, 11:46 AM
Sci Advisor
P: 3,313
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?
matqkks
#3
Feb19-12, 03:01 PM
P: 153
Sorry for being vague but I meant symbolically.

joeblow
#4
Feb19-12, 06:04 PM
P: 71
How do CAS evaluate derivatives

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.
pwsnafu
#5
Feb19-12, 10:26 PM
Sci Advisor
P: 838
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
[itex]\sin(x^2)+3[/itex]
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]


Register to reply

Related Discussions
ODE now made me think about derivatives and partial derivatives Calculus & Beyond Homework 6
Derivatives: Composites, normal lines, n-th derivatives and more. Calculus & Beyond Homework 5
Derivatives / partial derivatives rule Calculus & Beyond Homework 7
Difference between curly derivatives and ordinary d derivatives, when to use each? Introductory Physics Homework 2
Estimating partial derivatives/directional derivatives Calculus & Beyond Homework 1