Symbolic Differentiation

Symbolic differentiation is easy to do with patterns because there is a list of reduction patterns in calculus books:

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

( (deriv (+ ?u ?v) ?x)  (+ (deriv ?u ?x)
                           (deriv ?v ?x)) )
( (deriv (* ?u ?v) ?x)  (+ (* ?v (deriv ?u ?x))
                           (* ?u (deriv ?v ?x))) )

These formulas have the properties:

• the formulas are recursive

• the formula whose derivative is being taken gets smaller at each step.