The formal derivative of a polynomialp(x) = ao + atX + ... + a"x"over R is defined to
Chapter 34, Problem 34.13(choose chapter or problem)
The formal derivative of a polynomialp(x) = ao + atX + ... + a"x"over R is defined to bep'(x) = at + 2a2x + ... + na"x,,-t.Prove that[p(x) + q(x)]' = p'(x) + q'(x)and[p(x)q(x)]' = p(x)q'(x) + p'(x)q(x).(An application of formal derivatives will be given in Section 47.)
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