(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

f(x) = (1-x^{3})(2+x^{4})(3-x^{5})(4+x^{6})(5-x^{7})(6+x^{8})...(2n+1-x^{2n+3})

Find f ' (1).

2. Relevant equations

3. The attempt at a solution

f (1) = 0 because of the first term. Also the pattern is that terms with odd numbers have a subtraction sign and terms with even numbers have an addition sign.

I used logarithmic differentiation ("a" & "b" denote the terms of the original function in order to avoid rewriting all that):

ln y = ln a + ln b ...

y' * (1/y) = (1/a) + (1/b)...

y' = [(1/a) + (1/b)] * [y]

y'(1) = [(1/a) + (1/b)] * [y(1)

Since we already know y(1) = 0, y'(1) also equals 0.

Is this correct? Any help is much appreciated.

Edited:I just noticed that after differentiating, my first term would be [1/(1-x^{3})] and plugging 1 to x would give a fraction where 0 is the denominator. I guess that makes my solution incorrect?

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# Homework Help: Derivative of a infinite product (Challenge Q)

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