Symbolic Differentiation

Symbolic differentiation is a classic problem that illustrates the basic steps of problem reduction search.

Primitive subproblems:

d/dx(x) = 1

d/dx(c) = 0

Subproblem reductions:

d/dx(u + v)  =  d/dx(u) + d/dx(v)

d/dx(u * v)  =  u * d/dx(v) + v * d/dx(u)
In the case of d/dx(u + v), the simpler subproblems are the two smaller derivatives d/dx(u) and d/dx(v). The method of combining subproblem solutions is to add these two results ( algebraically, not numerically).

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