Question

I have to show that the relative error of the product of two positive numbers is aproximately to the sum of the relative errors of its factors.

My teacher told me to use first order approximation, but I don't know how to use it.Please help

Answer 1

(a + da)(b + db) = a b + b dz + a db + da db

da db is higher order
so
to first order error in product is
a db + b da

error/product = db/b + da/a