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Advanced Math/Chain rule with f(x) and g(x)


Hi Clyde

I don't really know how to find the derivative of a function like
[f(x)]^2/[g(2x)+2x] and need some help on it.

Thank you for your time,

To solve problems like this, you apply the usual rules for differentiation:

Quotient rule: (u/v)' = (u'v - uv')/v^2

Here, u=f(x)^2, so u' = 2f(x)f'(x) by the power & chain rules.

Similarly, v=g(2x)+2x, which is 2g'(2x)+2 by the chain rule.

So the answer would be:

[ 2f(x)f'(x)(g(2x)+2x) - f(x)^2 (2g'(2x)+2) ] / [ (2g'(2x)+2)^2 ]

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Clyde Oliver


I can answer all questions up to, and including, graduate level mathematics. I am more likely to prefer questions beyond the level of calculus. I can answer any questions, from basic elementary number theory like how to prove the first three digits of powers of 2 repeat (they do, with period 100, starting at 8), all the way to advanced mathematics like proving Egorov's theorem or finding phase transitions in random networks.


I am a PhD educated mathematician working in research at a major university.


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BA mathematics & physics, PhD mathematics from a top 20 US school.

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