I'm interested in building a derivative calculator. I've racked my brains over solving the problem, but I haven't found a right solution at all. May you have a hint how to start? Thanks
I'm sorry! I clearly want to make symbolic differentiation.
Let's say you have the function f(x) = x^3 + 2x^2 + x
I want to display the derivative, in this case f'(x) = 3x^2 + 4x + 1
I'd like to implement it in objective-c for the iPhone.
I assume that you're trying to find the exact derivative of a function. (Symbolic differentiation)
You need to parse the mathematical expression and store the individual operations in the function in a tree structure.
For example, x + sin²(x)
would be stored as a +
operation, applied to the expression x
and a ^
(exponentiation) operation of sin(x)
and 2
.
You can then recursively differentiate the tree by applying the rules of differentiation to each node. For example, a +
node would become the u' + v'
, and a *
node would become uv' + vu'
.