- #1
Jimmy84
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Homework Statement
if p(x) = f(x)/g(x)
Prove that
p'(x) = g(x) f '(x) - f(x) g '(x) / g(x)ˆ2
Homework Equations
The Attempt at a Solution
The proof goes like this in my book
p(x + h) - p(x) / h = [ f(x+h)/ g(x+h) - f(x) / g(x) ] / h
= f(x + h) g(x) - f(x) g(x + h) / h g(x) g(x + h)
I don't understand why did g(x) and g(x + h) appeared in the numerator on the last part of the proof? Since g(x) and g(x +h) were already multiplyed by h in the denominator.
Thanks in advance.